Inertia isolation error compensation system and method for biaxial rotation modulation inertial measurement unit

Abstract

The invention relates to the field of inertial navigation error compensation, in particular to an inertial isolation error compensation system and method of a double-shaft rotation modulation laser inertial measurement unit, and aims to solve the problems that due to inevitable installation errors of an existing double-shaft rotation modulation system, double shafts cannot completely isolate angular motion and ground velocity of a carrier, and navigation precision is limited. An error compensation system is composed of an IMU, a double-shaft rotating mechanism, a navigation computer, an inner frame angle measuring device, an inner frame driving motor, an outer frame angle measuring device and an outer frame driving motor. The method comprises the following steps: defining a coordinate system, finally calculating an inertial space isolation error caused by a shaft system installation error of an inner frame shaft and an outer frame shaft through an error matrix and a conversion matrix, and respectively superposing the isolation error as a compensation item into control instructions of an inner frame driving motor and an outer frame driving motor. According to the invention, through accurate modeling and real-time compensation of inertia isolation errors caused by shafting installation errors, the navigation precision and reliability are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to inertial navigation error compensation, in particular to an inertial isolation error compensation system and method for a dual-axis rotation modulated laser inertial unit. BACKGROUND

[0002] Rotation modulation technology is an effective way to improve the long-time navigation accuracy of inertial navigation systems. In recent years, a large amount of research and application work has been carried out on ships. This technology makes the IMU (Inertial Measurement Unit) rotate periodically around the axis, modulates the constant error of the inertial device into a periodic signal, and realizes the average and cancellation of the error in navigation calculation, achieving the error self-compensation function of the inertial unit. Without significantly increasing the manufacturing cost of the inertial device itself, the system accuracy is greatly improved.

[0003] In a dynamic carrier environment, the irregular angular motion of the carrier will seriously interfere with or even destroy the preset rotation modulation rule, thereby weakening the modulation effect. In order to solve this problem, rotation modulation technology based on carrier isolation has been applied and developed in single-axis, dual-axis and three-axis stable platforms in recent years. It can isolate the angular motion of the carrier corresponding to the rotation axis and eliminate the oscillation error caused by the angular motion of the carrier. For example, Chinese patent CN111964696A discloses a dual-axis rotation inertial navigation system carrier angular motion isolation modulation method. By analyzing the relationship between IMU sensitive data, carrier attitude and dual-axis rotation angle, the IMU sensitive angular rate is projected onto the dual-rotation axis, and the angle of the rotation shaft in the inertial space is integrated to obtain the angle. This method controls the rotation shaft to track the expected angle based on the inertial space rule change, realizes the isolation of the carrier angular motion, avoids the delay and cumulative error problem caused by angular rate control, and effectively reduces the negative impact of the carrier angular motion on the rotation modulation.

[0004] However, such existing isolation technology has a common and unsolved limitation: they are all based on the assumption that the dual-axis rotation mechanism is an ideal structure, without considering the installation error that inevitably exists in the actual machining and installation process of the inner frame shaft and the outer frame shaft. In a real dual-axis rotation modulation system, the inner frame shaft and the outer frame shaft inevitably have a small deviation and misalignment with the theoretical IMU coordinate system, i.e., there is an axis system installation error. Although these error angles are small, in high-precision long-time navigation applications, they will couple with carrier motion, earth rotation and other factors, causing the calculated "isolated angular velocity" to deviate from the ideal value. This deviation is not a periodic signal, but will accumulate over time, eventually destroying the periodic compensation characteristics of the rotation modulation on the constant error of the inertial device, limiting the further improvement of navigation accuracy. SUMMARY

[0005] The purpose of this invention is to solve the technical problem that existing dual-axis rotation modulation systems cannot completely isolate the angular motion and ground velocity of the carrier due to unavoidable installation errors, thus limiting navigation accuracy. The invention provides a dual-axis rotation modulation inertial navigation system and method for inertial isolation error compensation.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A dual-axis rotation modulation inertial navigation system with inertial isolation error compensation is characterized by including an IMU, a dual-axis rotation mechanism, and a navigation computer. The dual-axis rotation mechanism includes an inner frame shaft and an outer frame shaft; The IMU includes a laser gyroscope and an accelerometer; The laser gyroscope and accelerometer are both mounted on the inner frame shaft, and their data output terminals are respectively connected to the input terminals of the navigation computer, which are used to transmit the output data of the laser gyroscope and accelerometer to the navigation computer. An inner frame angle measuring device and an inner frame drive motor are mounted on the inner frame shaft; the control terminal of the inner frame drive motor is connected to the output terminal of the navigation computer and is used to drive the inner frame shaft to rotate; the data output terminal of the inner frame angle measuring device is connected to the input terminal of the navigation computer and is used to measure the rotation angle of the inner frame shaft in real time and transmit the rotation angle data to the navigation computer. An outer frame angle measuring device and an outer frame drive motor are mounted on the outer frame shaft; the control terminal of the outer frame drive motor is connected to the output terminal of the navigation computer and is used to drive the outer frame shaft to rotate; the data output terminal of the outer frame angle measuring device is connected to the input terminal of the navigation computer and is used to measure the rotation angle of the outer frame shaft in real time and transmit the rotation angle data to the navigation computer. The navigation computer is used to calculate the isolation error of the inner frame shaft and the outer frame shaft caused by the shaft system installation error based on the data received from the laser gyroscope, accelerometer, inner frame angle measuring device and outer frame angle measuring device, and to add the isolation error of the inner frame shaft and the outer frame shaft caused by the shaft system installation error as a compensation term to the control commands of the inner frame drive motor and the outer frame drive motor respectively, so as to compensate for the inertial isolation error of the dual-axis rotation modulation inertial group in real time.

[0007] Furthermore, the IMU is configured redundantly, containing M laser gyroscopes and accelerometers, where M > 3; The M laser gyroscopes and M accelerometers are mounted on the inner frame axis in a non-orthogonal symmetrical geometry.

[0008] Meanwhile, the present invention also provides a method for compensating for inertial isolation errors in a dual-axis rotationally modulated inertial navigation system, which is characterized by including the following steps: Step 1: Assemble the above-mentioned dual-axis rotation modulated inertial navigation system with inertial isolation error compensation. Step 2: Define the coordinate system of the dual-axis rotationally modulated inertial navigation system for inertial isolation error compensation. Define the geocentric inertial coordinate system as i, the navigation coordinate system as n, the IMU coordinate system as b, the vehicle coordinate system as p, the inner frame isometric coordinate system as s1, the inner frame axial coordinate system as b1, the outer frame isometric coordinate system as s2, and the outer frame axial coordinate system as b2. Step 3: Based on the installation errors of the inner and outer frame shafts, calculate the error matrix from the inner frame shaft's angular coordinate system s1 to the IMU coordinate system b. Error matrix from outer frame isometric angular coordinate system s2 to inner frame axial coordinate system b1 The installation error includes the inner frame axis's rotation around the IMU coordinate system b. shaft and Shaft installation error angle , With the outer frame axis about the inner frame axis coordinate system b1 shaft and The error angle of the shaft , ; Step 4: Based on the rotation angles obtained from the inner frame angle measuring device and the outer frame angle measuring device, establish the coordinate transformation relationship corresponding to the rotational motion of the inner frame axis and the outer frame axis, and calculate the transformation matrix from the inner frame axis angle measuring coordinate system s1 to the inner frame axis coordinate system b1. ; Step 5: Obtain the laser gyroscope-sensitive angular velocity by measuring the laser gyroscope. Therefore, based on the laser gyroscope's sensitive angular velocity Based on the error matrix and Transformation matrix Calculate the sensitive angular velocity of the laser gyroscope respectively. Projections in the inner frame isometric coordinate system s1 and the outer frame isometric coordinate system s2 and ; Step 6: Obtain the rotation angle from the inner frame angle measuring device. Error matrix and Transformation matrix and the laser gyroscope's sensitive angular velocity Substitute the laser gyroscope's sensitive angular velocity Projections in the inner frame isometric coordinate system s1 and the outer frame isometric coordinate system s2 and The isolation angular velocities of the inner frame shaft and the outer frame shaft, respectively, without considering shaft system installation errors, are obtained. and The isolation angular velocity of the inner frame shaft and outer frame shaft, taking into account shaft system installation errors. and ; Step 7: Calculate the isolation errors of the inner frame shaft and outer frame shaft caused by the shaft system installation error, respectively. and Among them, the inner frame shaft isolation error caused by shaft system installation error is The shaft isolation error of the outer frame caused by the shaft system installation error is: The isolation error of the inner frame shaft and the outer frame shaft is used as a compensation term and superimposed on the control commands of the inner frame drive motor and the outer frame drive motor respectively. The negative feedback compensation is used to control the inner frame drive motor and the outer frame drive motor to drive the inner frame shaft and the outer frame shaft to rotate in real time, thereby realizing the inertial isolation error compensation of the dual-axis rotation modulation inertial group.

[0009] Furthermore, in step 3, the error matrix from the inner frame isometric angular coordinate system s1 to the IMU coordinate system b... The transformation matrix from the outer frame isometric angular coordinate system s2 to the inner frame axial coordinate system b1 The calculation formulas are as follows: ; In the formula, and For the inner frame axis around the IMU coordinate system b shaft and Shaft installation error angle; ; In the formula, and The outer frame axis is in coordinate system b1 about the inner frame axis. shaft and The installation error angle of the shaft.

[0010] Furthermore, in step 4, the transformation matrix from the inner frame isometric angular coordinate system s1 to the inner frame axial coordinate system b1... The transformation matrix from the outer frame isometric angular coordinate system s2 to the outer frame axial coordinate system b2 The calculation formulas are as follows: ; In the formula, Let be the angle of rotation from the inner frame axis coordinate system b1 to the inner frame axis angular coordinate system s1 about the inner frame axis; ; In the formula, Let be the angle of rotation from the outer frame axis coordinate system b2 to the outer frame axis angular coordinate system s2 around the outer frame axis.

[0011] Furthermore, in step 5, the laser gyroscope is sensitive to the angular velocity. Projections in the inner frame isometric coordinate system s1 and the outer frame isometric coordinate system s2 and The calculation formulas are as follows: ; .

[0012] Furthermore, in step 6, the isolation angular velocities of the inner frame shaft and the outer frame shaft are not considered due to shaft system installation errors. and The calculation formulas are as follows: ; In the formula, For laser gyroscope sensitive angular velocity In IMU coordinate system b Projection of the axis; ; In the formula, The rotation angle obtained by the inner frame angle measuring device. and These are the laser gyroscope's sensitive angular velocities. In IMU coordinate system b shaft and Projection of the axis.

[0013] Furthermore, in step 6, the isolation angular velocities of the inner frame shaft and outer frame shaft are considered in relation to shaft system installation errors. and The calculation formulas are as follows: ; In the formula, and For the inner frame axis around the IMU coordinate system b shaft and Shaft installation error angle, , and These are the laser gyroscope's sensitive angular velocities. In IMU coordinate system b axis, shaft and Projection of the axis; ; In the formula, and The outer frame axis is in coordinate system b1 about the inner frame axis. shaft and The installation error angle of the shaft.

[0014] Furthermore, in step 7, the negative feedback compensation specifically refers to: In each control cycle, the navigation computer recalculates the inner frame axis isolation error based on the current measurement data. Isolation error with outer frame axis As a feedforward compensation or control correction, it is superimposed on the control commands of the inner frame drive motor and the outer frame drive motor, respectively. Through the control commands, the inner frame drive motor and the outer frame drive motor are controlled in real time to drive the inner frame shaft and the outer frame shaft to rotate, thereby realizing the inertial isolation error compensation of the dual-axis rotation modulation inertial group.

[0015] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention provides a dual-axis rotation modulation inertial group inertial isolation error compensation system. Through the design architecture of IMU, dual-axis rotation mechanism and navigation computer, it compensates for the non-periodic isolation error caused by the coupling of frame angular motion, carrier motion and Earth rotation caused by the installation error of inner frame axis and outer frame axis. This further suppresses the divergence trend of navigation error and significantly improves navigation accuracy and reliability in long-endurance and high-dynamic environments.

[0016] (2) The present invention provides a dual-axis rotation modulation inertial group inertial isolation error compensation system. Through the redundant configuration of the IMU system, it realizes the synergistic enhancement of "high reliability of redundant configuration" and "high precision of rotation modulation and error compensation", providing the ultimate solution for application scenarios with extreme requirements for reliability and precision (such as aerospace and marine).

[0017] (3) The present invention provides a dual-axis rotation modulation inertial group inertial isolation error compensation method. By establishing a complete coordinate system transformation chain, it accurately calculates and feeds back the isolation error caused by the axis installation error, thereby achieving complete isolation of the two axes in inertial space. This can eliminate the "divergence trend" of the error accumulating over time from the root, ensuring the effectiveness of the rotation modulation periodic compensation characteristics, and thus achieving the goal of improving the accuracy of long-endurance navigation.

[0018] (4) The present invention provides a dual-axis rotation modulation inertial group inertial isolation error compensation method. By giving a simplified error matrix formula, the complex installation error influence is linearized, which greatly reduces the complexity of real-time calculation and computer load, so that high-precision error compensation can be quickly realized in the navigation computer, ensuring the real-time performance of the compensation. At the same time, the compensation matrix form of the outer frame shaft system installation error is clarified, ensuring the coordinate transformation accuracy from the inner frame to the outer frame, and forming a complete compensation model for the installation error of the entire dual-axis rotation mechanism.

[0019] (5) The present invention provides a method for compensating for the isolation error of a dual-axis rotation modulated inertial navigation system. This method clarifies the complete projection path of the sensitive angular rate of the laser gyroscope, ensuring that all motion components (carrier motion, Earth rotation, and relative rotation) can be accurately mapped onto the control axis, even when considering installation errors. This lays a theoretical foundation for the accurate calculation of the isolation error. Furthermore, it clarifies the functional relationship between the isolation error and the carrier motion, Earth rotation, and inner frame angle, revealing the coupling effect mechanism of installation errors. This makes the compensation method not only effective against static errors but also adaptable to complex, dynamically changing environments. Attached Figure Description

[0020] Figure 1 This is a schematic diagram illustrating the transformation relationship between various coordinate systems in an embodiment of the dual-axis rotation modulation inertial navigation system inertial isolation error compensation method of the present invention; Figure 2 This is a schematic diagram illustrating the spatial relationship between the geocentric inertial coordinate system i, the navigation coordinate system n, and the carrier coordinate system p in an embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the relationship between the dual-axis coordinate system s and the IMU coordinate system b in an embodiment of the present invention; Figure 4 This is a schematic diagram showing the comparison results of the horizontal comprehensive error of 100 Monte Carlo simulation navigation tests in an embodiment of the present invention; Figure 5 This is a schematic diagram showing the comparison between the speed error without compensation for shaft system installation error and the speed error with compensation for shaft system installation error in a simulated navigation in an embodiment of the present invention; Figure 6 This is a schematic diagram showing the comparison between the positional error of the uncompensated shaft system installation error and the positional error of the compensated shaft system installation error in a simulated navigation scenario according to an embodiment of the present invention. Detailed Implementation

[0021] To better understand the purpose, structure, and function of this invention, the following detailed description of a dual-axis rotation modulation inertial navigation system and method for inertial isolation error compensation, in conjunction with the accompanying drawings, is provided.

[0022] This invention discloses a dual-axis rotation modulation inertial group inertial isolation error compensation system for compensating for inertial isolation errors of a dual-axis rotation modulation inertial group, comprising: an IMU, a dual-axis rotation mechanism, and a navigation computer.

[0023] The dual-axis rotation mechanism includes an inner frame axis and an outer frame axis; the IMU includes a laser gyroscope and an accelerometer; both the laser gyroscope and the accelerometer are mounted on the inner frame axis, and their data output terminals are respectively connected to the input terminals of the navigation computer to transmit the output data of the laser gyroscope and the accelerometer to the navigation computer.

[0024] An inner frame angle measuring device and an inner frame drive motor are mounted on the inner frame shaft. The control terminal of the inner frame drive motor is connected to the output terminal of the navigation computer to drive the inner frame shaft to rotate. The data output terminal of the inner frame angle measuring device is connected to the input terminal of the navigation computer to measure the rotation angle of the inner frame shaft in real time and transmit the rotation angle data to the navigation computer. An outer frame angle measuring device and an outer frame drive motor are mounted on the outer frame shaft. The control terminal of the outer frame drive motor is connected to the output terminal of the navigation computer to drive the outer frame shaft to rotate. The data output terminal of the outer frame angle measuring device is connected to the input terminal of the navigation computer to measure the rotation angle of the outer frame shaft in real time and transmit the rotation angle data to the navigation computer.

[0025] The navigation computer is used to calculate the isolation error of the inner frame shaft and the outer frame shaft caused by the shaft system installation error based on the data received from the laser gyroscope, accelerometer, inner frame angle measuring device and outer frame angle measuring device. The isolation error of the inner frame shaft and the outer frame shaft caused by the shaft system installation error is used as a compensation term and superimposed on the control commands of the inner frame drive motor and the outer frame drive motor respectively, so as to compensate for the inertial isolation error of the dual-axis rotation modulation inertial group in real time.

[0026] In this embodiment, the IMU includes three laser gyroscopes and three accelerometers, which are mounted on the inner frame axis in a triaxial orthogonal arrangement.

[0027] In other embodiments, the IMU includes M laser gyroscopes and M accelerometers, where M > 3; the M laser gyroscopes and M accelerometers are mounted on the inner frame axis in a non-orthogonal symmetrical geometry, which can be a tetrahedral arrangement or a dodecahedral arrangement, and their equivalent constant error is modulated by a dual-axis rotation mechanism.

[0028] The present invention discloses a method for compensating for inertial isolation errors in a dual-axis rotationally modulated inertial navigation system, the specific steps of which are as follows: Step 1: Assemble the above-mentioned dual-axis rotation modulated inertial navigation system with inertial isolation error compensation. Step 2: Define the coordinate system of the dual-axis rotationally modulated inertial navigation system for inertial isolation error compensation. Here, the geocentric inertial coordinate system is defined as i, which is a coordinate system that does not move relative to inertial space; its origin is located at the Earth's center of mass. The axis is along the Earth's axis of rotation. The plane is located on the Earth's equatorial plane.

[0029] Define the navigation coordinate system (i.e., the geographic coordinate system) as n, with the axes of the navigation coordinate system (i.e., the geographic coordinate system) n being North, Sky, and East; its origin is at the center of mass of the moving vehicle. Upward along the perpendicular line of the gravitational field, Heading north along the meridian, Heading east along the latitude line.

[0030] Define the IMU coordinate system as b, and define IMU coordinate system b as fixed to the inertial navigation system body; its origin is at the inertial navigation system's center of mass. shaft and The input axes of the directional accelerometers are aligned. The shaft is located at direction and Within the plane defined by the input axis of the directional acceleration meter, This forms a right-handed rectangular coordinate system.

[0031] Define the carrier coordinate system as P, with the origin of the carrier coordinate system P set at the inertial navigation centroid. shaft and The input axes of the directional accelerometers are aligned. Axis perpendicular to The axis lies within the longitudinal plane of symmetry of the projectile. This forms a right-handed rectangular coordinate system.

[0032] Define a dual-axis coordinate system as s. When the inner and outer frame axes in the dual-axis coordinate system s have no installation error and are at zero position relative to the IMU coordinate system, the inner frame axis and the IMU coordinate system... The axes coincide, and the outer frame axes are aligned with the IMU coordinate system. Axis coincidence.

[0033] Define the inner frame isometric coordinate system as s1. The inner frame isometric coordinate system s1 is fixedly connected to the inner frame isometric rotation axis, causing the IMU to rotate together. When the inner frame isometric coordinate system s1 has an installation error relative to the IMU coordinate system, define the inner frame axis around the IMU coordinate system... The installation error angle of the shaft is The inner frame axis revolves around the IMU coordinate system The installation error angle of the shaft is .

[0034] When the inner frame is at its zero-position, the inner frame isometric coordinate system s1 is the inner frame axial coordinate system b1; therefore, there is only one rotation angle about the inner frame axis between the inner frame axial coordinate system b1 and the inner frame isometric coordinate system s1, and this rotation angle about the inner frame axis is defined as... Counterclockwise is positive.

[0035] Define the outer frame isometric coordinate system as s2. The outer frame isometric coordinate system s2 is fixedly connected to the outer frame's rotation axis, causing the inner frame to rotate together. When there is an installation error between the outer frame isometric coordinate system s2 and the inner frame isometric coordinate system b1, define the outer frame axis around the inner frame isometric coordinate system b1. The installation error angle of the shaft is The outer frame axis revolves around the inner frame axis in coordinate system b1. The installation error angle of the shaft is .

[0036] When the outer frame angle measurement is at zero position, the outer frame isometric coordinate system s2 is the outer frame axial coordinate system b2. Therefore, there is only one rotation angle about the outer frame axis between the outer frame axial coordinate system b2 and the outer frame isometric coordinate system s2. This rotation angle about the outer frame axis is defined as... Counterclockwise is positive.

[0037] Figure 1 This is a schematic diagram illustrating the transformation relationships between the coordinate systems mentioned above; Figure 2 This is a schematic diagram showing the relationship between the geocentric inertial coordinate system i, the navigation coordinate system n, and the vehicle coordinate system p. Figure 3 This is a schematic diagram of the spatial relationship between the dual-axis coordinate system s and the IMU coordinate system b.

[0038] Step 3: Based on the installation errors of the inner and outer frame shafts and the definition of the dual-axis coordinate system, the inner frame shaft is rotated around the IMU coordinate system b. shaft and Shaft installation error angle , And rotate first Then rotate The error matrix from the inner frame isometric angular coordinate system s1 to the IMU coordinate system b can be obtained as follows: The calculation formula is as follows: ; because and Since both are small quantities, the above formula can be simplified to: ; Then, through the outer frame axis around the inner frame axis coordinate system b1 shaft and The error angle of the shaft , And rotate first Then rotate The error matrix from the outer frame isometric angular coordinate system s2 to the inner frame axial coordinate system b1 can be obtained as follows: ; because and Since both are small quantities, the above formula can be simplified to: .

[0039] Step 4: Based on the rotation angles obtained from the inner frame angle measuring device and the outer frame angle measuring device, calculate the transformation matrix from the inner frame isometric coordinate system s1 to the inner frame axial coordinate system b1. The transformation matrix from the outer frame isometric angular coordinate system s2 to the outer frame axial coordinate system b2 ; The transformation matrix from the inner frame isometric angular coordinate system s1 to the inner frame axial coordinate system b1 is: ; The transformation matrix from the outer frame isometric angular coordinate system s2 to the outer frame axial coordinate system b2 is: .

[0040] Step 5: Obtain the laser gyroscope-sensitive angular velocity by measuring the laser gyroscope. Therefore, based on the laser gyroscope's sensitive angular velocity Based on the error matrix and Transformation matrix Calculate the sensitive angular velocity of the laser gyroscope respectively. Projections in the inner frame isometric coordinate system s1 and the outer frame isometric coordinate system s2 and ; Among them, due to the angular velocity sensitive to the carrier's motion, the laser gyroscope... Caused by the angular motion of the carrier, the angular velocity that the laser gyroscope is sensitive to. Let be the angular velocity of the carrier coordinate system p relative to the geocentric inertial coordinate system i. The derivation process is as follows: First, let the rotational angular velocity of the carrier coordinate system p relative to the navigation coordinate system n be... The rotational angular velocity of the IMU coordinate system b relative to the carrier coordinate system p caused by the rotation of the inner and outer frame axes. The angular velocity of the navigation coordinate system n relative to the geocentric inertial coordinate system i, caused by the motion of the carrier lines and the Earth's rotation, is determined by... Composition, in which The amount is small, so its impact is negligible. To achieve biaxial inertial isolation, it is necessary to... and Compensation is performed, where the laser gyroscope is sensitive to the angular velocity. It can be expressed by the following formula: ; In the formula, Let be the transformation matrix from the carrier coordinate system p to the IMU coordinate system b. Transformation matrix from navigation coordinate system n to vehicle coordinate system p; Transformation matrix from vehicle coordinate system p to IMU coordinate system b The calculation formula is as follows: ; In the formula, Let p be the transformation matrix from the carrier coordinate system p to the outer frame axis coordinate system b2. Since the outer frame axis is fixed to the carrier, then... .

[0041] Based on coordinate transformation relationships, the laser gyroscope is sensitive to the angular velocity. Projection in the inner frame isometric coordinate system s1 The calculation formula is as follows: ; In the formula, The error matrix is ​​the distance from the inner frame isometric angular coordinate system s1 to the IMU coordinate system b. Angular velocity sensitive by laser gyroscope Projection in the inner frame isometric coordinate system s2 The calculation formula is as follows: .

[0042] Step 6: Obtain the rotation angle from the inner frame angle measuring device. Error matrix and Transformation matrix and the laser gyroscope's sensitive angular velocity Substitute the laser gyroscope sensitive angular velocity from step 5 Projections in the inner frame isometric coordinate system s1 and the outer frame isometric coordinate system s2 and If we disregard shaft installation errors, we can obtain the isolation angular velocities of the inner frame shaft and the outer frame shaft. and The calculation formulas are as follows: ; In the formula, Let the angular velocity of the carrier coordinate system p relative to the geocentric inertial coordinate system i be in the IMU coordinate system b. Projection of the axis; ; In the formula, Let be the angle of rotation from the inner frame axial coordinate system b1 to the inner frame angular coordinate system s1 about the inner frame axis. and These represent the angular velocities of the carrier coordinate system p relative to the geocentric inertial coordinate system i in the IMU coordinate system b. shaft and Projection of the axis.

[0043] If shaft installation errors are taken into account, the isolation angular velocities of the inner frame shaft and the outer frame shaft can be obtained. and The calculation formulas are as follows: ; In the formula, and For the inner frame axis around the IMU coordinate system b shaft and Shaft installation error angle, , and These represent the angular velocities of the carrier coordinate system p relative to the geocentric inertial coordinate system i in the IMU coordinate system b. axis, shaft and Projection of the axis; ; In the formula, and The outer frame axis is in coordinate system b1 about the inner frame axis. shaft and The installation error angle of the shaft.

[0044] Step 7: Calculate the isolation errors of the inner frame shaft and outer frame shaft caused by the shaft system installation error, respectively. and Among them, the inner frame shaft isolation error caused by shaft system installation error is: The shaft isolation error of the outer frame caused by the shaft system installation error is: ; Substituting the relevant formulas from step 6, we can see that the isolation error between the inner frame shaft and the outer frame shaft caused by the shaft system installation error... and The calculation formulas are as follows: ; ; As can be seen from the above formula, the isolation error is not only related to the shaft system installation error, but also to the carrier motion, the Earth's rotation, and the rotation angle of the inner frame shaft. The isolation angle error increases continuously over time, affecting the periodic compensation characteristics of rotation modulation. Therefore, to improve the navigation accuracy of long-endurance guidance systems, it is necessary to compensate for the isolation error, specifically the isolation error between the inner and outer frame shafts caused by the shaft system installation error. and The calculation results are used as compensation terms for the isolation of the inner frame axis and the outer frame axis and stored in the navigation computer. They are then superimposed on the control commands of the inner frame drive motor and the outer frame drive motor, respectively. The negative feedback compensation is used to control the inner frame drive motor and the outer frame drive motor to rotate the inner frame axis and the outer frame axis in real time, thereby realizing the inertial isolation error compensation of the dual-axis rotation modulation inertial group.

[0045] The negative feedback compensation is performed in real time. Specifically, the navigation computer recalculates the inner frame axis isolation error based on the current measurement data in each control cycle. Isolation error with outer frame axis As a feedforward compensation or control correction, it is superimposed on the control commands of the inner frame drive motor and the outer frame drive motor, respectively. Through the control commands, the inner frame drive motor and the outer frame drive motor are controlled in real time to drive the inner frame shaft and the outer frame shaft to rotate, thereby realizing the inertial isolation error compensation of the dual-axis rotation modulation inertial group.

[0046] To verify the effectiveness and superiority of the dual-axis rotation modulation inertial navigation system (INS) inertial isolation error compensation method of the present invention, the navigation systems with uncompensated shaft installation error and compensated shaft installation error inertial isolation schemes were simulated and compared, based on the error characteristics of the inertial navigation system and the sensitive information of the IMU.

[0047] The simulation conditions are as follows: the constant error of the three laser gyroscopes is 0.01° / h, and the standard deviation of white noise is 0.01° / h; the constant error of the three accelerometers is 1×10⁻⁵ m / s², and the standard deviation of white noise is 3×10⁻⁵ m / s²; the installation error of the four axes of the inner and outer frames is 100″; the initial attitude angles are all 0°; the disturbances of the carrier's pitch, yaw, and roll angles are all sinusoidal variations with a frequency of 2.5Hz and an amplitude of 1° / s; the initial velocity of the inertial navigation system is 0; the simulation duration is 6000s.

[0048] Simulation results are shown below Figures 4 to 6 .

[0049] in, Figure 4 This paper presents the results of 100 Monte Carlo simulations comparing an inertial isolation scheme that compensates for shaft installation errors and an inertial isolation scheme that does not compensate for shaft installation errors, as described in the embodiment of the dual-axis rotation modulation inertial navigation system (INS) error compensation method of the present invention. The simulations focus on the overall error in the horizontal direction. As shown in the figure, the overall error of the inertial isolation scheme that compensates for shaft installation errors is reduced by 10% to 20% compared to the uncompensated scheme. Figure 4 The phenomenon that the error of the inertial isolation scheme that compensates for shaft installation error is greater than the error of the inertial isolation scheme that does not compensate for shaft installation error in the horizontal direction comprehensive error is caused by random noise and does not affect the conclusion.

[0050] Figure 5 This is a schematic diagram showing the comparison of speed errors between uncompensated and compensated shaft system installation errors in a simulated navigation scenario according to an embodiment of the present invention. It can be seen that the speed error accuracy of the compensated shaft system installation error is significantly higher than that of the uncompensated shaft system installation error.

[0051] Figure 6 This is a schematic diagram showing the comparison of position errors between uncompensated and compensated shaft system installation errors in a simulated navigation scenario according to an embodiment of the present invention. It can be seen that the position error accuracy of the compensated shaft system installation error is significantly higher than that of the uncompensated shaft system installation error.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. 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 or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A dual-axis rotationally-modulated inertial- unit inertial-isolation error compensation system characterized by: The system comprises an IMU, a double-axis rotating mechanism and a navigation computer. The double-axis rotating mechanism comprises an inner frame shaft and an outer frame shaft. The IMU comprises a laser gyroscope and an accelerometer. The laser gyroscope and the accelerometer are both mounted on the inner frame shaft, and their data output ends are connected with the input ends of the navigation computer respectively, so as to transmit the output data of the laser gyroscope and the accelerometer to the navigation computer. An inner frame angle measuring device and an inner frame driving motor are mounted on the inner frame shaft, the control end of the inner frame driving motor is connected with the output end of the navigation computer, so as to drive the inner frame shaft to rotate, and the data output end of the inner frame angle measuring device is connected with the input end of the navigation computer, so as to measure the rotation angle of the inner frame shaft in real time and transmit the rotation angle data to the navigation computer. An outer frame angle measuring device and an outer frame driving motor are mounted on the outer frame shaft, the control end of the outer frame driving motor is connected with the output end of the navigation computer, so as to drive the outer frame shaft to rotate, and the data output end of the outer frame angle measuring device is connected with the input end of the navigation computer, so as to measure the rotation angle of the outer frame shaft in real time and transmit the rotation angle data to the navigation computer. The navigation computer is used to calculate the isolation error of the inner frame shaft and the outer frame shaft caused by the shaft system installation error according to the data received from the laser gyroscope, the inner frame angle measuring device and the outer frame angle measuring device, and superimpose the isolation error of the inner frame shaft and the outer frame shaft caused by the shaft system installation error as a compensation term into the control instructions of the inner frame driving motor and the outer frame driving motor respectively, so as to compensate the inertial isolation error of the double-axis rotating modulation inertial measurement unit in real time.

2. The double-axis rotating modulation inertial measurement unit inertial isolation error compensation system according to claim 1, wherein: The IMU adopts a redundant configuration and comprises M laser gyroscopes and M accelerometers, wherein M>3. The M laser gyroscopes and the M accelerometers are mounted on the inner frame shaft in a non-orthogonal symmetrical geometric structure.

3. A dual-axis rotation modulated inertial measurement unit (IMU) inertial isolation error compensation method, characterized in that, The method comprises the following steps: Step 1: assembling the double-axis rotating modulation inertial measurement unit inertial isolation error compensation system according to claim 1 or 2; Step 2: defining the coordinate system of the double-axis rotating modulation inertial measurement unit inertial isolation error compensation system; defining the geocentric inertial coordinate system as i, the navigation coordinate system as n, the IMU coordinate system as b, the carrier coordinate system as p, the inner frame shaft angle measuring coordinate system as s1, the inner frame shaft coordinate system as b1, the outer frame shaft angle measuring coordinate system as s2 and the outer frame shaft coordinate system as b2; Step 3, calculating an error matrix of the inner frame axis angular coordinate system s1 to the IMU coordinate system b and an error matrix of the outer frame axis angular coordinate system s2 to the inner frame axis coordinate system b1 according to installation errors of the inner frame axis and the outer frame axis ; wherein the installation errors include installation error angles of the inner frame axis around the axis and axis of the IMU coordinate system b , and error angles of the outer frame axis around the axis and axis of the inner frame axis coordinate system b1 , ;​ Step 4, according to the rotation angles obtained by the inner frame goniometer device and the outer frame goniometer device, a coordinate conversion relationship corresponding to the rotation movements of the inner frame shaft and the outer frame shaft is established, and a conversion matrix from the inner frame shaft goniometric coordinate system s1 to the inner frame shaft coordinate system b1 is calculated ; Step 5, obtaining the laser gyro sensitive angular velocity by laser gyro measurement , and calculating the laser gyro sensitive angular velocity , based on the error matrix and the conversion matrix ; and , respectively, projecting the laser gyro sensitive angular velocity in the inner frame axis angular coordinate system s1 and the outer frame axis angular coordinate system s2 and ; Step 6, the rotation angle obtained by the inner frame angle measurement device , the error matrix and , the conversion matrix and the angular velocity sensitive to the laser gyroscope substitute the angular velocity sensitive to the laser gyroscope projection of the inner frame axis and the outer frame axis in the inner frame axis coordinate system s1 and the outer frame axis coordinate system s2 and respectively, the isolated angular velocity of the inner frame axis and the outer frame axis without considering the shaft system installation error and and the isolated angular velocity of the inner frame axis and the outer frame axis considering the shaft system installation error and ; Step 7, calculate the isolation error of the inner frame shaft and the outer frame shaft caused by the shafting installation error respectively and wherein the isolation error of the inner frame shaft caused by the shafting installation error is ; the isolation error of the outer frame shaft caused by the shafting installation error is ; and superimposing the isolation error of the inner frame shaft and the outer frame shaft as a compensation term into the control instructions of the inner frame driving motor and the outer frame driving motor respectively, and performing negative feedback compensation to control the inner frame driving motor and the outer frame driving motor to drive the inner frame shaft and the outer frame shaft to rotate in real time, so as to realize the double-axis rotating modulation inertial measurement unit inertial isolation error compensation.

4. The dual-axis rotational modulation inertial- isolation error compensation method of claim 3, wherein, In step 3, the error matrix of the inner-frame axis-angle coordinate system s1 to the IMU coordinate system b and the error matrix of the outer-frame axis-angle coordinate system s2 to the inner-frame axis coordinate system b1 are respectively calculated as follows: ； In the formula, and are the installation error angles of the axis and axis of the inner frame shaft around the IMU coordinate system b; ； In the formula, and are the installation error angles of the outer frame axis around the inner frame axis coordinate system b1 axis and axis.

5. The dual-axis rotational modulation inertial- isolation error compensation method of claim 4, wherein, In Step 4, the conversion matrix of the inner frame axis angular coordinate system s1 to the inner frame axis coordinate system b1 and the conversion matrix of the outer frame axis angular coordinate system s2 to the outer frame axis coordinate system b2 are respectively calculated as follows: ； In the formula, is the angle of rotation of the inner frame axis coordinate system b1 to the inner frame axis spherical coordinate system s1 about the inner frame axis. ； In the formula, is the angle of rotation of the outer frame axis coordinate system b2 to the outer frame axis spherical coordinate system s2 about the outer frame axis.

6. The dual-axis rotational modulation inertial- isolation error compensation method of claim 5, wherein, In step 5, the laser gyro is sensitive to angular velocity The projection of the inner frame axis-angle coordinate system s1 and the outer frame axis-angle coordinate system s2 is And The calculation formula is respectively: ； 。 7. The dual-axis rotational modulation inertial- isolated error compensation method of claim 6, wherein, In step 6, the isolated angular velocity of the inner frame shaft and the outer frame shaft without considering the shafting installation error is calculated as follows: and respectively. ； wherein is the sensitive angular velocity of the laser gyro in the IMU coordinate system b projection of the axis ； wherein is the rotation angle obtained by the inner frame goniometer device, and are the sensitive angular velocities of the laser gyro, respectively are the projections of the axes of the IMU coordinate system b and onto the axes of the inner frame coordinate system 8. The dual-axis rotational modulation inertial- isolation error compensation method of claim 6, wherein, In step 6, the isolated angular velocity of the inner frame shaft and the outer frame shaft considering the shafting installation error is calculated and The calculation formula is respectively ； In the formula, and are the installation error angles of the axis and axis of the inner frame shaft around the IMU coordinate system b, , and are the sensitive angular velocities of the laser gyro, are the projections of the axis, axis and axis of the IMU coordinate system b on the inner frame coordinate system b. ； In the formula, and are the installation error angles of the outer frame axis around the inner frame axis coordinate system b1 axis and axis.

9. The double-axis rotating modulation inertial measurement unit inertial isolation error compensation method according to any one of claims 3-8, wherein: In step 7, the negative feedback compensation is specifically: The navigation computer recalculates the inner frame axis isolation error and the outer frame axis isolation error according to the current measurement data in each control cycle and superimposes the inner frame axis isolation error and the outer frame axis isolation error as feedforward compensation or control correction to control instructions of the inner frame driving motor and the outer frame driving motor respectively to control the inner frame driving motor and the outer frame driving motor in real time through the control instructions to drive the inner frame shaft and the outer frame shaft to rotate, so as to realize the dual-axis rotation modulation inertial isolation error compensation of the inertial measurement unit.

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