Low-altitude aircraft silicon optical gyro inertial navigation error compensation method

Abstract

The application relates to a silicon optical gyro inertial navigation error compensation method for low-altitude aircraft, a deterministic error model is constructed through static calibration, initial compensation is carried out on zero offset, scale factor error and installation error, and main system errors in a static working condition are eliminated; a random error time-varying evolution model containing temperature, vibration and motion working condition coupling influence is constructed, time-varying nonlinear characteristics of random error are described through partial derivatives, and high-precision dynamic compensation of the random error is realized; inertial navigation attitude updating is carried out based on angular velocity data after random error compensation, absolute position data collected by GNSS, motion speed data obtained through visual auxiliary positioning calculation, closed-loop correction of inertial navigation error state is realized through Kalman filtering, and finally high-precision navigation results are obtained; the technical scheme provided by the application can effectively overcome the defects that high-precision and real-time compensation of silicon optical gyro inertial navigation error is difficult in the prior art.

Description

Technical Field

[0001] This invention relates to silicon photonic gyroscope inertial navigation, and more specifically to a method for error compensation of silicon photonic gyroscope inertial navigation in low-altitude aircraft. Background Technology

[0002] When low-altitude aircraft (such as small UAVs and multi-rotor aircraft) operate in complex low-altitude environments (such as urban canyons and areas obscured by near-ground obstacles), GNSS signals are easily interfered with, making the inertial navigation system (INS) a core guarantee for navigation. Silicon photonic gyroscopes (MEMS gyroscopes) are widely used in the INS systems of low-altitude aircraft due to their small size, low power consumption, and low cost. However, due to the influence of manufacturing processes, ambient temperature, vibration and shock, and complex low-altitude motion conditions, their output exhibits significant deterministic errors (such as zero bias, scale factor error, and installation error) and random errors (such as angular random walk, zero bias instability, and rate random walk). These errors accumulate over time, severely affecting the positioning and attitude determination accuracy of the INS.

[0003] Existing inertial navigation error compensation schemes mostly employ fixed parameter models (such as static zero-bias compensation, linear scaling factor correction, etc.) or traditional Kalman filtering algorithms. These schemes have the following drawbacks:

[0004] 1) Static calibration parameters cannot adapt to error changes under the motion conditions of low-altitude aircraft, especially the nonlinear drift of errors caused by temperature and vibration;

[0005] 2) Traditional Kalman filtering algorithms do not fully utilize the time-varying evolution characteristics of inertial navigation errors, resulting in insufficient accuracy in modeling the time-varying patterns of errors;

[0006] 3) There is a lack of a layered compensation mechanism for high-frequency noise and low-frequency drift in silicon photonic gyroscopes, and residual error accumulation still exists after compensation.

[0007] To address the aforementioned issues, this invention proposes a method for compensating errors in the inertial navigation of silicon photonic gyroscopes for low-altitude aircraft. Through multi-stage error modeling, dynamic calibration, and filtering compensation based on partial derivative optimization, high-precision, real-time compensation of silicon photonic gyroscope inertial navigation errors is achieved. Summary of the Invention

[0008] (a) Technical problems to be solved

[0009] In view of the above-mentioned shortcomings of the existing technology, the present invention provides a method for compensating for silicon photonic gyroscope inertial navigation errors in low-altitude aircraft, which can effectively overcome the shortcomings of the existing technology in that it is difficult to perform high-precision, real-time compensation for silicon photonic gyroscope inertial navigation errors.

[0010] (II) Technical Solution

[0011] To achieve the above objectives, the present invention provides the following technical solution:

[0012] A method for compensating for inertial navigation errors in silicon optical gyroscopes of low-altitude aircraft includes the following steps:

[0013] S1. Collect raw data from silicon photonic gyroscopes and their associated sensors, remove outliers, and standardize the data.

[0014] S2. Construct a deterministic error model through static calibration to initially compensate for zero bias, scale factor error and installation error, thereby eliminating the main systematic errors under static operating conditions.

[0015] S3. Construct a time-varying evolution model of random error that includes the coupled effects of temperature, vibration and motion conditions, and characterize the time-varying nonlinear characteristics of random error through partial derivatives to achieve high-precision dynamic compensation of random error.

[0016] S4. Based on the angular velocity data after random error compensation, the inertial navigation attitude is updated. Combined with the absolute position data collected by GNSS and the motion velocity data obtained by visual-assisted positioning, the inertial navigation error state is closed-loop corrected through Kalman filtering to obtain the final high-precision navigation result.

[0017] S5. Evaluate the effect of inertial navigation error compensation, and dynamically optimize the random error prediction equation based on the evaluation results to achieve adaptive optimization of inertial navigation error compensation.

[0018] Preferably, in S1, the raw data of the silicon photonic gyroscope and its associated sensors are collected, outliers are removed, and the data is standardized, including:

[0019] S11. Acquire angular velocity data from the silicon optical gyroscope. Simultaneously, full data from the accompanying accelerometer was collected. raw Temperature data T from the temperature sensor, absolute position data collected by GNSS, and motion velocity data obtained from visual-assisted positioning calculations;

[0020] S12. Remove impulsive outliers from the angular velocity data;

[0021] S13. Convert the angular velocity data after removing outliers into a unified physical dimension, and align the collected data with timestamps according to the inertial navigation sampling frequency to construct an original data set containing time series.

[0022] Where, ω x,raw ω y,raw ω z,raw These are the angular velocity values ​​for the X-axis, Y-axis, and Z-axis, respectively.

[0023] Preferably, removing pulse-like outliers from the angular velocity data in S12 includes:

[0024] The 3σ criterion is used to remove impulsive outliers from the angular velocity data, and the mean μ of the angular velocity sequence is calculated. ω and standard deviation σ ω If the collected angular velocity data ω i,raw satisfy Then determine the i-th angular velocity data ω i,raw These are pulse-type outliers and are removed.

[0025] Preferably, in S13, the angular velocity data after outlier removal is converted into a unified physical dimension, and the acquired data is timestamped according to the inertial navigation sampling frequency to construct an original data set containing time series, including:

[0026] The original data set D is represented by the following formula: ; Among them, t k For the k-th inertial navigation sampling time, ω raw (t k ) represents the angular velocity data at the k-th inertial navigation sampling time, a raw (t k T(t) represents the full data at the k-th inertial navigation sampling time. k ) represents the temperature data at the k-th inertial navigation sampling time, and N is the total number of sampling points.

[0027] Preferably, in S2, a deterministic error model is constructed through static calibration to initially compensate for zero bias, scale factor error, and installation error, thereby eliminating the main systematic errors under static operating conditions, including: S21. Fix the inertial navigation system on a horizontal turntable and rotate it around the three axes at multiple angles in sequence to collect static and angular velocity data at different speeds. S22. Construct a deterministic error model for the silicon optical gyroscope: ; Where, ω static Angular velocity data after system error compensation, K is a 3×3 error matrix composed of scaling factor error and installation error, and b is the three-axis zero bias vector; S23. The least squares method is used to solve for the error matrix K and the three-axis zero bias vector b, and the optimal parameters are obtained by fitting multiple sets of calibration data. S24. Substitute the solved error matrix K and the three-axis zero-bias vector b into the deterministic error model of the silicon optical gyroscope to perform systematic error compensation on all angular velocity data in the original dataset D. The angular velocity data at the k-th inertial navigation sampling time after systematic error compensation is ω. static (t k ).

[0028] Preferably, in S3, a time-varying evolution model of random error is constructed, incorporating the coupled effects of temperature, vibration, and motion conditions. Partial derivatives characterize the time-varying nonlinear properties of the random error, achieving high-precision dynamic compensation for the random error, including: S31. The random errors of silicon optical gyroscopes include angular random walk (ARW), bias instability (BI), and rate random walk (RRW), and are affected by temperature T(t) and vibration acceleration a. v (t) and rate of change of angular velocity The coupling effect exhibits time-varying nonlinear characteristics, so a time-varying evolution model of random error of silicon optical gyroscope is constructed: ; Where t represents time, ω err (t) represents the random error of the silicon photonic gyroscope, ε(·) represents the nonlinear error function of multivariable coupling, and vibration acceleration is the pure vibration component extracted from the full data of the accelerometer. S32, In order to characterize the random error ω err The time-varying nonlinear characteristics of (t) introduce a random error ω. err (t) Using the partial derivatives with respect to each influencing factor, construct the time-varying evolution equation of random error: ; Where, dω err This is the differential change of the random error. Let dT be the first partial derivative of the random error with respect to temperature, i.e., the temperature offset coefficient, and let dT be the differential change in temperature. da is the first partial derivative of the random error with respect to the vibration acceleration, i.e., the vibration sensitivity coefficient. v This is the differential change in vibration acceleration. This is the first partial derivative of the random error with respect to the rate of change of angular velocity, i.e., the angular acceleration sensitivity coefficient. The differential change in the rate of change of angular velocity. This represents the second-order partial derivative of the random error with respect to the coupling of temperature and vibration acceleration. This is the second-order partial derivative of the random error with respect to the coupling of temperature and the rate of change of angular velocity. This is the second-order partial derivative of the random error with respect to the coupling of vibration acceleration and the rate of change of angular velocity; S33. Discretize the time-varying evolution equation of random error and construct a recursive form of the random error prediction equation: ; in, , The predicted random error values ​​ΔT are the k-th and (k+1)-th inertial navigation sampling times, respectively. k Let be the temperature change at the k-th inertial navigation sampling time. , T(t k ), T(t) k+1 () represents the temperature data at the k-th and (k+1)-th inertial navigation sampling times, respectively; △a v,k Let be the change in vibration acceleration at the k-th inertial navigation sampling time. a v (t k ), a v (t k+1 ) are the vibration accelerations at the kth and (k+1)th inertial navigation sampling times, respectively; Let be the change in the rate of change of angular velocity at the k-th inertial navigation sampling time. , , These are the rates of change of angular velocity at the k-th and (k+1)-th inertial navigation sampling times, respectively; S34. The recursive least squares method combined with the random error prediction sequence is used to update the first-order and second-order partial derivatives in the random error prediction equation in real time, so as to realize the dynamic adaptation of model parameters. S35. Predict the random error value at the k-th inertial navigation sampling time. The angular velocity data ω at the k-th inertial navigation sampling time after system error compensation static (t k After removing the random error, the angular velocity data ω at the k-th inertial navigation sampling time is obtained. comp (t k ): .

[0029] Preferably, in step S4, the inertial navigation attitude is updated based on the angular velocity data after random error compensation. Combined with the absolute position data acquired by GNSS and the motion velocity data obtained from visual-assisted positioning, a Kalman filter is used to achieve closed-loop correction of the inertial navigation error state, resulting in the final high-precision navigation result, including: S41. The angular velocity data ω at the k-th inertial navigation sampling time after random error compensation is processed using the quaternion method. comp (t k Perform attitude calculation: ; Where q(t) k Let q(t) be the attitude quaternion at the k-th inertial navigation sampling time. k )=[q0(t k ),q1(t k ),q2(t k ),q3(t k )] T ,q0(tk ) represents the scalar part, q1(t) k ), q2(t k ), q3(t k The vector part is used to describe the attitude of the low-altitude aircraft in three-dimensional space. The scalar and vector parts together are used to describe the attitude of the low-altitude aircraft. Let q(t) be the attitude quaternion at the k-th inertial navigation sampling time. k The time derivative of ) Represents quaternion multiplication; S42. The attitude quaternion q(t) at the (k+1)th inertial navigation sampling time is recursively derived using the Runge-Kutta method. k+1 ): ; Where △t is the time interval; S43. Combine attitude quaternions and acceleration data to calculate the predicted position and predicted velocity. Subtract the predicted position and predicted velocity from the absolute position data collected by GNSS and the motion velocity data obtained by visual-assisted positioning to obtain the prediction residual. Then, use extended Kalman filtering to make the optimal estimate of the inertial navigation error state vector. S44. Feedback the inertial navigation error state vector to the inertial navigation solution module to obtain the final high-precision navigation result.

[0030] Preferably, in step S5, the inertial navigation error compensation effect is evaluated, and the random error prediction equation is dynamically optimized based on the evaluation results to achieve adaptive optimization of the inertial navigation error compensation, including: S51. Select multi-dimensional evaluation indicators to evaluate the effect of inertial navigation error compensation; S52. When the inertial navigation error compensation effect does not meet the requirements, S3 is executed again, and the first-order partial derivatives and second-order partial derivatives in the random error prediction equation are updated to optimize the random error prediction equation. S53. Through multiple iterative updates, the random error prediction equation is adapted to the motion conditions and environmental conditions of the low-altitude aircraft, thereby achieving adaptive optimization of inertial navigation error compensation.

[0031] Preferably, in S51, multi-dimensional evaluation indicators are selected to evaluate the inertial navigation error compensation effect, including: The root mean square of attitude angle error, root mean square of position error, root mean square of velocity error, and standard deviation of angular velocity error are selected as evaluation indicators. At the same time, a threshold is set for each evaluation indicator. If any one of the evaluation indicators exceeds its threshold, the inertial navigation error compensation effect is determined to be unsatisfactory.

[0032] (III) Beneficial Effects Compared with the prior art, the silicon optical gyroscope inertial navigation error compensation method for low-altitude aircraft provided by the present invention has the following beneficial effects: 1) This invention effectively characterizes the time-varying nonlinearity and multi-factor coupling characteristics of silicon photonic gyroscope errors by combining static deterministic error compensation and dynamic random error compensation with random error time-varying evolution modeling based on partial derivative optimization, thus solving the problem that traditional fixed parameter models cannot adapt to dynamic motion conditions. 2) By introducing the partial derivatives of random errors with respect to various influencing factors, it is possible to accurately predict random errors under the coupling of temperature, vibration and motion conditions. Compared with the traditional linear error compensation model, the compensation accuracy is improved by more than 30%. 3) By combining Kalman filter closed-loop correction and model adaptive optimization mechanism, real-time suppression and long-term stability control of inertial navigation error are achieved, which significantly reduces the accumulation of navigation error of low-altitude aircraft; 4) The present invention has a clear logic, strong data reusability in each link, and is easy to be engineered and implemented in existing low-altitude aircraft inertial navigation systems, and has high practical value. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0034] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0036] The following describes the specific process of the silicon photonic gyroscope inertial navigation error compensation method for low-altitude aircraft provided by this invention, using a specific example (e.g.) Figure 1 (as shown) and technical effects.

[0037] S1. Collect raw data from the silicon photonic gyroscope and its associated sensors, remove outliers, and standardize the data, including: S11. Acquire angular velocity data from the silicon optical gyroscope. Simultaneously, full data from the accompanying accelerometer was collected. rawTemperature data T from the temperature sensor, absolute position data collected by GNSS, and motion velocity data obtained from visual-assisted positioning calculations; S12. Remove impulsive outliers from the angular velocity data; S13. Convert the angular velocity data after removing outliers into a unified physical dimension, and align the collected data with timestamps according to the inertial navigation sampling frequency to construct an original data set containing time series. Where, ω x,raw ω y,raw ω z,raw These are the angular velocity values ​​for the X-axis, Y-axis, and Z-axis, respectively.

[0038] Specifically, S12 removes pulse-like outliers from the angular velocity data, including: The 3σ criterion is used to remove impulsive outliers from the angular velocity data, and the mean μ of the angular velocity sequence is calculated. ω and standard deviation σ ω If the collected angular velocity data ω i,raw satisfy Then determine the i-th angular velocity data ω i,raw These are pulse-type outliers and are removed.

[0039] Specifically, in S13, the angular velocity data after outlier removal is converted into a unified physical dimension, and the acquired data is timestamped according to the inertial navigation sampling frequency to construct a raw data set containing time series, including: The original data set D is represented by the following formula: ; Among them, t k For the k-th inertial navigation sampling time, ω raw (t k ) represents the angular velocity data at the k-th inertial navigation sampling time, a raw (t k T(t) represents the full data at the k-th inertial navigation sampling time. k ) represents the temperature data at the k-th inertial navigation sampling time, and N is the total number of sampling points.

[0040] S2. Construct a deterministic error model through static calibration to initially compensate for zero bias, scale factor errors, and installation errors, eliminating the main systematic errors under static operating conditions, including: S21. Fix the inertial navigation system on a horizontal turntable and rotate it around the three axes at multiple angles in sequence to collect static and angular velocity data at different speeds. S22. Construct a deterministic error model for the silicon optical gyroscope: ; Where, ωstatic Angular velocity data after system error compensation, K is a 3×3 error matrix composed of scaling factor error and installation error, and b is the three-axis zero bias vector; S23. The least squares method is used to solve for the error matrix K and the three-axis zero bias vector b, and the optimal parameters are obtained by fitting multiple sets of calibration data. S24. Substitute the solved error matrix K and the three-axis zero-bias vector b into the deterministic error model of the silicon optical gyroscope to perform systematic error compensation on all angular velocity data in the original dataset D. The angular velocity data at the k-th inertial navigation sampling time after systematic error compensation is ω. static (t k ).

[0041] S3. Construct a time-varying evolution model of random errors that incorporates the coupled effects of temperature, vibration, and motion conditions. Use partial derivatives to characterize the time-varying nonlinear characteristics of random errors, achieving high-precision dynamic compensation for random errors, including: S31. The random errors of silicon optical gyroscopes include angular random walk (ARW), bias instability (BI), and rate random walk (RRW), and are affected by temperature T(t) and vibration acceleration a. v (t) and rate of change of angular velocity The coupling effect exhibits time-varying nonlinear characteristics, so a time-varying evolution model of random error of silicon optical gyroscope is constructed: ; Where t represents time, ω err (t) represents the random error of the silicon photonic gyroscope, ε(·) represents the nonlinear error function of multivariable coupling, and vibration acceleration is the pure vibration component extracted from the full data of the accelerometer. S32, In order to characterize the random error ω err The time-varying nonlinear characteristics of (t) introduce a random error ω. err (t) Using the partial derivatives with respect to each influencing factor, construct the time-varying evolution equation of random error: ; Where, dω err This is the differential change of the random error. Let dT be the first partial derivative of the random error with respect to temperature, i.e., the temperature offset coefficient, and let dT be the differential change in temperature. da is the first partial derivative of the random error with respect to the vibration acceleration, i.e., the vibration sensitivity coefficient. v This is the differential change in vibration acceleration. This is the first partial derivative of the random error with respect to the rate of change of angular velocity, i.e., the angular acceleration sensitivity coefficient. The differential change in the rate of change of angular velocity. This represents the second-order partial derivative of the random error with respect to the coupling of temperature and vibration acceleration. This is the second-order partial derivative of the random error with respect to the coupling of temperature and the rate of change of angular velocity. This is the second-order partial derivative of the random error with respect to the coupling of vibration acceleration and the rate of change of angular velocity; S33. Discretize the time-varying evolution equation of random error and construct a recursive form of the random error prediction equation: ; in, , The predicted random error values ​​ΔT are the k-th and (k+1)-th inertial navigation sampling times, respectively. k Let be the temperature change at the k-th inertial navigation sampling time. , T(t k ), T(t) k+1 () represents the temperature data at the k-th and (k+1)-th inertial navigation sampling times, respectively; △a v,k Let be the change in vibration acceleration at the k-th inertial navigation sampling time. a v (t k ), a v (t k+1 ) are the vibration accelerations at the kth and (k+1)th inertial navigation sampling times, respectively; Let be the change in the rate of change of angular velocity at the k-th inertial navigation sampling time. , , These are the rates of change of angular velocity at the k-th and (k+1)-th inertial navigation sampling times, respectively; S34. The recursive least squares method combined with the random error prediction sequence is used to update the first-order and second-order partial derivatives in the random error prediction equation in real time, so as to realize the dynamic adaptation of model parameters. S35. Predict the random error value at the k-th inertial navigation sampling time. The angular velocity data ω at the k-th inertial navigation sampling time after system error compensation static (t k After removing the random error, the angular velocity data ω at the k-th inertial navigation sampling time is obtained. comp (t k ): .

[0042] In this technical solution, static deterministic error compensation and dynamic random error compensation are combined with time-varying evolution modeling of random errors based on partial derivative optimization. This effectively characterizes the time-varying nonlinearity and multi-factor coupling characteristics of silicon photonic gyroscope errors, solving the problem that traditional fixed-parameter models cannot adapt to dynamic motion conditions. Furthermore, by introducing the partial derivatives of random errors with respect to various influencing factors, the random errors under the coupling of temperature, vibration, and motion conditions can be accurately predicted.

[0043] S4. Based on the angular velocity data after random error compensation, the inertial navigation attitude is updated. Combining the absolute position data acquired by GNSS and the motion velocity data obtained from visual-assisted positioning, a Kalman filter is used to achieve closed-loop correction of the inertial navigation error state, resulting in the final high-precision navigation result, including: S41. The angular velocity data ω at the k-th inertial navigation sampling time after random error compensation is processed using the quaternion method. comp (t k Perform attitude calculation: ; Where q(t) k Let q(t) be the attitude quaternion at the k-th inertial navigation sampling time. k )=[q0(t k ),q1(t k ),q2(t k ),q3(t k )] T ,q0(t k ) represents the scalar part, q1(t) k ), q2(t k ), q3(t k The vector part is used to describe the attitude of the low-altitude aircraft in three-dimensional space. The scalar and vector parts together are used to describe the attitude of the low-altitude aircraft. Let q(t) be the attitude quaternion at the k-th inertial navigation sampling time. k The time derivative of ) Represents quaternion multiplication; S42. The attitude quaternion q(t) at the (k+1)th inertial navigation sampling time is recursively derived using the Runge-Kutta method. k+1 ): ; Where △t is the time interval; S43. Combine attitude quaternions and acceleration data to calculate the predicted position and predicted velocity. Subtract the predicted position and predicted velocity from the absolute position data collected by GNSS and the motion velocity data obtained by visual-assisted positioning to obtain the prediction residual. Then, use extended Kalman filtering to make the optimal estimate of the inertial navigation error state vector. S44. Feedback the inertial navigation error state vector to the inertial navigation solution module to obtain the final high-precision navigation result.

[0044] S5. Evaluate the effectiveness of inertial navigation error compensation, and dynamically optimize the random error prediction equation based on the evaluation results to achieve adaptive optimization of inertial navigation error compensation, including: S51. Select multi-dimensional evaluation indicators to evaluate the effect of inertial navigation error compensation; S52. When the inertial navigation error compensation effect does not meet the requirements, S3 is executed again, and the first-order partial derivatives and second-order partial derivatives in the random error prediction equation are updated to optimize the random error prediction equation. S53. Through multiple iterative updates, the random error prediction equation is adapted to the motion conditions and environmental conditions of the low-altitude aircraft, thereby achieving adaptive optimization of inertial navigation error compensation.

[0045] Specifically, S51 selects multi-dimensional evaluation indicators to evaluate the inertial navigation error compensation effect, including: The root mean square of attitude angle error, root mean square of position error, root mean square of velocity error, and standard deviation of angular velocity error are selected as evaluation indicators. At the same time, a threshold is set for each evaluation indicator. If any one of the evaluation indicators exceeds its threshold, the inertial navigation error compensation effect is determined to be unsatisfactory.

[0046] In the technical solution of this application, by combining Kalman filter closed-loop correction and model adaptive optimization mechanism, real-time suppression and long-term stability control of inertial navigation error are achieved, which significantly reduces the accumulation of navigation error of low-altitude aircraft.

[0047] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for compensating errors in the inertial navigation of a silicon optical gyroscope for low-altitude aircraft, characterized in that: Includes the following steps: S1. Collect raw data from silicon photonic gyroscopes and their associated sensors, remove outliers, and standardize the data. S2. Construct a deterministic error model through static calibration to initially compensate for zero bias, scale factor error and installation error, thereby eliminating the main systematic errors under static operating conditions. S3. Construct a time-varying evolution model of random error that includes the coupled effects of temperature, vibration and motion conditions, and characterize the time-varying nonlinear characteristics of random error through partial derivatives to achieve high-precision dynamic compensation of random error. S4. Based on the angular velocity data after random error compensation, the inertial navigation attitude is updated. Combined with the absolute position data collected by GNSS and the motion velocity data obtained by visual-assisted positioning, the inertial navigation error state is closed-loop corrected through Kalman filtering to obtain the final high-precision navigation result. S5. Evaluate the effect of inertial navigation error compensation, and dynamically optimize the random error prediction equation based on the evaluation results to achieve adaptive optimization of inertial navigation error compensation.

2. The method for compensating errors in the silicon photonic gyroscope inertial navigation of low-altitude aircraft according to claim 1, characterized in that: The raw data from the silicon photonic gyroscope and its associated sensors are collected in S1, outliers are removed, and the data is standardized, including: S11. Acquire angular velocity data from the silicon optical gyroscope. Simultaneously, full data from the accompanying accelerometer was collected. raw Temperature data T from the temperature sensor, absolute position data collected by GNSS, and motion velocity data obtained from visual-assisted positioning calculations; S12. Remove impulsive outliers from the angular velocity data; S13. Convert the angular velocity data after removing outliers into a unified physical dimension, and align the collected data with timestamps according to the inertial navigation sampling frequency to construct an original data set containing time series. Where, ω x,raw ω y,raw ω z,raw These are the angular velocity values ​​for the X-axis, Y-axis, and Z-axis, respectively.

3. The method for compensating errors in the silicon photonic gyroscope inertial navigation of low-altitude aircraft according to claim 2, characterized in that: S12 removes pulse-like outliers from angular velocity data, including: The 3σ criterion is used to remove impulsive outliers from the angular velocity data, and the mean μ of the angular velocity sequence is calculated. ω and standard deviation σ ω If the collected angular velocity data ω i,raw satisfy Then determine the i-th angular velocity data ω i,raw These are pulse-type outliers and are removed.

4. The method for compensating errors in the silicon photonic gyroscope inertial navigation of a low-altitude aircraft according to claim 3, characterized in that: In S13, the angular velocity data after outlier removal is converted into a unified physical dimension, and the acquired data is timestamped according to the inertial navigation sampling frequency to construct a raw data set containing time series, including: The original data set D is represented by the following formula: ； Among them, t k For the k-th inertial navigation sampling time, ω raw (t k ) represents the angular velocity data at the k-th inertial navigation sampling time, a raw (t k T(t) represents the full data at the k-th inertial navigation sampling time. k ) represents the temperature data at the k-th inertial navigation sampling time, and N is the total number of sampling points.

5. The method for compensating errors in the silicon photonic gyroscope inertial navigation of a low-altitude aircraft according to claim 4, characterized in that: In S2, a deterministic error model is constructed through static calibration to initially compensate for zero bias, scale factor errors, and installation errors, eliminating the main systematic errors under static operating conditions, including: S21. Fix the inertial navigation system on a horizontal turntable and rotate it around the three axes at multiple angles in sequence to collect static and angular velocity data at different speeds. S22. Construct a deterministic error model for the silicon optical gyroscope: ； Where, ω static Angular velocity data after system error compensation, K is a 3×3 error matrix composed of scaling factor error and installation error, and b is the three-axis zero bias vector; S23. The least squares method is used to solve for the error matrix K and the three-axis zero bias vector b, and the optimal parameters are obtained by fitting multiple sets of calibration data. S24. Substitute the solved error matrix K and the three-axis zero-bias vector b into the deterministic error model of the silicon optical gyroscope to perform systematic error compensation on all angular velocity data in the original dataset D. The angular velocity data at the k-th inertial navigation sampling time after systematic error compensation is ω. static (t k ).

6. The method for compensating for silicon optical gyroscope inertial navigation errors in low-altitude aircraft according to claim 5, characterized in that: S3 constructs a time-varying evolution model of random errors that incorporates the coupled effects of temperature, vibration, and motion conditions. Partial derivatives characterize the time-varying nonlinear properties of random errors, enabling high-precision dynamic compensation of random errors, including: S31. The random errors of silicon optical gyroscopes include angular random walk (ARW), bias instability (BI), and rate random walk (RRW), and are affected by temperature T(t) and vibration acceleration a. v (t) and rate of change of angular velocity The coupling effect exhibits time-varying nonlinear characteristics, so a time-varying evolution model of random error of silicon optical gyroscope is constructed: ； Where t represents time, ω err (t) represents the random error of the silicon photonic gyroscope, ε(·) represents the nonlinear error function of multivariable coupling, and vibration acceleration is the pure vibration component extracted from the full data of the accelerometer. S32, In order to characterize the random error ω err The time-varying nonlinear characteristics of (t) introduce a random error ω. err (t) Using the partial derivatives with respect to each influencing factor, construct the time-varying evolution equation of random error: ； Where, dω err This is the differential change of the random error. Let dT be the first partial derivative of the random error with respect to temperature, i.e., the temperature offset coefficient, and let dT be the differential change in temperature. da is the first partial derivative of the random error with respect to the vibration acceleration, i.e., the vibration sensitivity coefficient. v This is the differential change in vibration acceleration. This is the first partial derivative of the random error with respect to the rate of change of angular velocity, i.e., the angular acceleration sensitivity coefficient. The differential change in the rate of change of angular velocity. This represents the second-order partial derivative of the random error with respect to the coupling of temperature and vibration acceleration. This is the second-order partial derivative of the random error with respect to the coupling of temperature and the rate of change of angular velocity. This is the second-order partial derivative of the random error with respect to the coupling of vibration acceleration and the rate of change of angular velocity; S33. Discretize the time-varying evolution equation of random error and construct a recursive form of the random error prediction equation: ； in, , The predicted random error values ​​ΔT are the k-th and (k+1)-th inertial navigation sampling times, respectively. k Let be the temperature change at the k-th inertial navigation sampling time. , T(t k ), T(t) k+1 () represents the temperature data at the k-th and (k+1)-th inertial navigation sampling times, respectively; △a v,k Let be the change in vibration acceleration at the k-th inertial navigation sampling time. a v (t k ), a v (t k+1 ) are the vibration accelerations at the kth and (k+1)th inertial navigation sampling times, respectively; Let be the change in the rate of change of angular velocity at the k-th inertial navigation sampling time. , , These are the rates of change of angular velocity at the k-th and (k+1)-th inertial navigation sampling times, respectively; S34. The recursive least squares method combined with the random error prediction sequence is used to update the first-order and second-order partial derivatives in the random error prediction equation in real time, so as to realize the dynamic adaptation of model parameters. S35. Predict the random error value at the k-th inertial navigation sampling time. The angular velocity data ω at the k-th inertial navigation sampling time after system error compensation static (t k After removing the random error, the angular velocity data ω at the k-th inertial navigation sampling time is obtained. comp (t k ): 。 7. The method for compensating errors in the silicon photonic gyroscope inertial navigation of a low-altitude aircraft according to claim 6, characterized in that: In S4, the inertial navigation attitude is updated based on the angular velocity data after random error compensation. Combined with the absolute position data acquired by GNSS and the motion velocity data obtained from visual-assisted positioning, a Kalman filter is used to achieve closed-loop correction of the inertial navigation error state, resulting in the final high-precision navigation result, including: S41. The angular velocity data ω at the k-th inertial navigation sampling time after random error compensation is processed using the quaternion method. comp (t k Perform attitude calculation: ； Where q(t) k Let q(t) be the attitude quaternion at the k-th inertial navigation sampling time. k )=[q0(t k ),q1(t k ),q2(t k ),q3(t k )] T ,q0(t k ) represents the scalar part, q1(t) k ), q2(t k ), q3(t k The vector part is used to describe the attitude of the low-altitude aircraft in three-dimensional space. The scalar and vector parts together are used to describe the attitude of the low-altitude aircraft. Let q(t) be the attitude quaternion at the k-th inertial navigation sampling time. k The time derivative of ) Represents quaternion multiplication; S42. The attitude quaternion q(t) at the (k+1)th inertial navigation sampling time is recursively derived using the Runge-Kutta method. k+1 ): ； Where △t is the time interval; S43. Combine attitude quaternions and acceleration data to calculate the predicted position and predicted velocity. Subtract the predicted position and predicted velocity from the absolute position data collected by GNSS and the motion velocity data obtained by visual-assisted positioning to obtain the prediction residual. Then, use extended Kalman filtering to make the optimal estimate of the inertial navigation error state vector. S44. Feedback the inertial navigation error state vector to the inertial navigation solution module to obtain the final high-precision navigation result.

8. The method for compensating errors in the silicon photonic gyroscope inertial navigation of a low-altitude aircraft according to claim 7, characterized in that: In S5, the effectiveness of inertial navigation error compensation is evaluated, and the random error prediction equation is dynamically optimized based on the evaluation results to achieve adaptive optimization of inertial navigation error compensation, including: S51. Select multi-dimensional evaluation indicators to evaluate the effect of inertial navigation error compensation; S52. When the inertial navigation error compensation effect does not meet the requirements, S3 is executed again, and the first-order partial derivatives and second-order partial derivatives in the random error prediction equation are updated to optimize the random error prediction equation. S53. Through multiple iterative updates, the random error prediction equation is adapted to the motion conditions and environmental conditions of the low-altitude aircraft, thereby achieving adaptive optimization of inertial navigation error compensation.

9. The method for compensating for silicon photonic gyroscope inertial navigation errors in low-altitude aircraft according to claim 8, characterized in that: S51 selects multi-dimensional evaluation indicators to evaluate the effect of inertial navigation error compensation, including: The root mean square of attitude angle error, root mean square of position error, root mean square of velocity error, and standard deviation of angular velocity error are selected as evaluation indicators. At the same time, a threshold is set for each evaluation indicator. If any one of the evaluation indicators exceeds its threshold, the inertial navigation error compensation effect is determined to be unsatisfactory.

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