An aerial calibration method for an outer frame azimuth axis dual-axis rotating inertial navigation system

Abstract

This invention relates to an aerial calibration method for a frame-based azimuth-axis dual-axis rotating inertial navigation system (RINS), belonging to the field of inertial navigation system calibration technology. The method includes: S10, IMU calibration error modeling; S20, design of a moving base azimuth-position observation method; S30, design of measurement equations based on an incremental structure; S40, Kalman filter design, including Kalman state equation design and Kalman measurement equation design; and S50, aerial calibration rotation path design. Using this aerial calibration method for the frame-based azimuth-axis dual-axis rotating inertial navigation system, it is possible to achieve full error parameter calibration of the IMU, thereby achieving non-disassembly-free calibration of the frame-based azimuth-axis dual-axis RINS in non-laboratory environments. This solves the problems of cumbersome calibration and difficult field-level calibration of the frame-based azimuth-axis dual-axis rotating inertial navigation system.

Description

Technical Field

[0001] This invention belongs to the field of inertial navigation system calibration technology, and specifically relates to an aerial calibration method for a frame-oriented dual-axis rotating inertial navigation system. Background Technology

[0002] The calibration accuracy of the Inertial Measurement Unit (IMU) determines the upper limit of the navigation accuracy of the Inertial Navigation System (INS). INS calibration techniques can be mainly divided into three categories: discrete calibration, model observation calibration, and system-level calibration. Among them, system-level calibration is a calibration method based on the INS error model. It establishes navigation error and device error models for the INS, employs a suitable rotation path, and utilizes Kalman filtering technology to estimate the error parameters of the inertial devices. This method is simple to operate and has low requirements for the turntable, thus it is widely used in laboratory environments or field calibration. In recent years, with the application of rotation modulation technology, rotating INS has developed rapidly due to its high navigation performance and low manufacturing cost advantages. The introduction of rotation mechanisms has made field calibration of INS without disassembly possible.

[0003] Currently, system-level calibration of inertial navigation systems (INS) is performed using either a three-axis or a two-axis turntable. For two-axis rotational inertial navigation systems (RINS), there are two main structural forms of the two-axis rotation mechanism. One uses the inner frame as the azimuth axis and the outer frame as the pitch axis (called the inner frame azimuth axis type two-axis rotation mechanism). This rotation structure can achieve IMU rotation around any axis, and its function is no different from a three-axis turntable. Most current two-axis rotational inertial navigation systems use this structure for system-level calibration. However, in certain applications, such as optoelectronic pod systems based on integrated inertial navigation / starlight systems, to meet the requirements of the optical system, such as preventing the optical field of view from being obstructed by the rotation structure at certain locations, a two-axis rotation mechanism with the inner frame as the horizontal axis and the outer frame as the azimuth axis is often used (called the outer frame azimuth axis type two-axis rotation mechanism). An inertial navigation system employing an outer frame azimuth-axis dual-axis rotating mechanism is called an outer frame azimuth-axis dual-axis rotating inertial navigation system, or simply an outer frame azimuth-axis dual-axis RINS. Because the pitch axis of an outer frame azimuth-axis dual-axis RINS is always horizontal, and the azimuth and roll axes can only rotate around the yaw axis, its structural characteristics determine that the pitch axis accelerometer of the RINS cannot sensitively detect changes in gravity in a static environment, and the roll and azimuth axis gyroscopes cannot rotate around the horizontal axis. This, in turn, leads to limitations in some accelerometer calibration parameters. and δK Ax2 The gyroscope's calibration parameters are not observable. and The poor observability is a major drawback of the outer frame orientation axis dual-axis indexing mechanism. Therefore, a non-disassembly field calibration method for the outer frame orientation axis dual-axis RINS still needs to be solved. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the purpose of this invention is to provide an aerial calibration method for an outer frame orientation axis dual-axis rotating inertial navigation system, so as to solve the defects existing in the prior art.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: an aerial calibration method for an outer frame azimuth axis type dual-axis rotating inertial navigation system, comprising: S10, IMU calibration error modeling: Define a coordinate system and establish a dual-axis RINS IMU calibration error model based on the coordinate system; S20. Design of the azimuth-position observation method for the moving base: Using GPS position and azimuth information as reference information, the position measurement equation and attitude measurement equation of the moving base are derived, thereby establishing the relationship between the inertial navigation calibration error and the position / azimuth reference information. S30. Measurement equation design based on incremental structure: Integrate the position measurement equation and the attitude measurement equation to obtain the integral measurement equation; Discretize the integral measurement equation to obtain the incremental measurement equation that is easy for computer processing; The incremental measurement equation reduces the influence of GPS position and orientation information measurement noise. S40. Kalman Filter Design: Based on the IMU calibration error model, design the Kalman filter state equation; based on the incremental measurement equation, design the Kalman filter measurement equation; use the Kalman filter composed of the Kalman filter state equation and the Kalman filter measurement equation to filter and estimate the various IMU calibration error quantities of the dual-axis RINS, and obtain the Kalman filter estimate. S50. Design of airborne calibration and transposition path: Design an airborne calibration and transposition path for the aircraft carrier. The airborne calibration and transposition path is used to fully excite the IMU calibration error and ensure that the Kalman filter estimate converges fully.

[0006] Preferably, in step S10, the coordinate system includes a geocentric inertial coordinate system, an Earth coordinate system, an IMU coordinate system, a gyroscope-sensitive coordinate system, an accelerometer-sensitive coordinate system, an aircraft carrier coordinate system, a turntable zero-position coordinate system, a navigation coordinate system, and a navigation calculation coordinate system, respectively denoted as i-system, e-system, b-system, g-system, a-system, m-system, m0-system, n-system, and n′-system, with specific definitions as follows: i series: origin o i Centered on Earth, oi x i and o i y i The axis lies in the plane of the Earth's equator, o i x i The axis points to the vernal equinox, o i z i The axis is the Earth's rotation axis and points towards the North Pole; all inertial device measurement information is based on the i-frame as the reference. e-series: Origin o e Located at the center of the Earth, o e x e The axis lies in the equatorial plane and points towards the central meridian. e z e The axis is along the direction of Earth's rotation, o e x e o e y e and o e z e The relationship between the three axes satisfies the right-hand rule; b series: Origin o b Located in the sensitive center of the IMU, o b x b Axis, o b y b axis and o b z b The axes are respectively aligned with the horizontal axis to the right, the vertical axis forward, and the vertical axis upward, forming a right-front-upper coordinate system; g series: o g x g Axis, o g y g axis and o g z g The axes are respectively aligned with the three gyroscope sensing axes; a series: o a x a Axis, o a y a axis and o a z a The axes are respectively aligned with the sensing axes of the three accelerometers; m-system: Origin o m Located at the sensitive center of the carrier, o m x m Axis, o m y m axis and o m z m The axes are respectively positioned to the right along the horizontal axis of the carrier, forward along the vertical axis, and upward along the vertical axis, forming a right-front-upper coordinate system; m0 system: origin o m0 Located at the center of rotation of the turntable, o m0 xm0 Axis, o m0 y m0 axis and o m0 z m0 The axes are respectively aligned to the right along the horizontal axis, forward along the vertical axis, and upward along the vertical axis of the turntable at the zero position, forming a right-front-upper coordinate system; n-system: adopts the Northeast-Heavenly Geographic Coordinate System; n′ system: The northeastern geographic coordinate system calculated using an inertial navigation system.

[0007] Preferably, in step S10, the IMU calibration error model is specifically as follows: in: and δK represents the true angular velocity and measured angular velocity of the three-axis gyroscope, respectively. G The gyroscope scaling and the gyroscope non-orthogonal error matrix are shown. This indicates that the three-axis gyroscope has zero bias. and δK represents the true specific force and the measured specific force of the triaxial accelerometer, respectively. A For the accelerometer scaling and non-orthogonal error matrix, This indicates that the triaxial accelerometer has zero bias. This indicates the quadratic error of the triaxial accelerometer. This indicates the specific force sensitive to the inner rod of the accelerometer; Let δK be a matrix composed of the squared terms of the accelerometer-sensitive specific force. A2 =[δK Ax2 δK Ay2 δK Az2 ] T The error coefficient for the quadratic term. The error coefficient of the inner lever arm of the accelerometer. This is the inner arm of a triaxial accelerometer; Among them, the gyroscope scale and the gyroscope non-orthogonal error matrix δK G Accelerometer scaling and non-orthogonal error matrix δK A They are represented as follows: Therefore, the measurement error model of the IMU is expressed as: Furthermore, the above formula can be summarized as follows: in:

[0008] Preferably, the specific method of step S20 includes: S21. In a dynamic environment, first measure and compensate for the lever error between the GPS antenna and the rotation center of the turntable, and then derive the position measurement equation. S22. Using the aircraft base orientation and attitude information provided by the dual-antenna GPS and the relative attitude information provided by the rotation mechanism, the attitude measurement equation is derived.

[0009] Preferably, in step S21, the position measurement equation is expressed as: In the formula: Where (·×) denotes antisymmetric matrix operation; For the inertial navigation misalignment angle, δp=[δL δλδh] T For positional error, For IMU three-axis external lever arm, The error is represented by the IMU three-axis external boom, where L represents latitude, h represents altitude, and R... M R represents the radius of curvature of the meridional circle. N This represents the radius of curvature of the zonal loop.

[0010] Preferably, in step S22, the derivation process of the attitude measurement equation is as follows: For a dual-axis RINS, the demodulated m0-series directional cosine array Represented as: in: In the formula: φ1=[0 Δφ y1 Δφ z1 ] T Let φ2 be the installation error vector between the IMU and the inner frame axis of the indexing mechanism. x2 Δφ y2 0] T This is the installation error vector between the inner frame shaft and the outer frame shaft of the indexing mechanism; Considering the actual If there are errors in north finding and attitude maintenance, then Represented as: therefore, Further expressed as: in: Let φ be the installation error angle between the m-system and the m0-system. mis =[φ misx φ misy φ misz ] T Then the attitude of the aircraft's moving base carrier at time t can be written as: in: According to the matrix chain multiplication rule, the GPS output base attitude... Approximately expressed as: in: in, Let be the azimuth angle output by the GPS at time t. and Let m0 represent the pitch and roll angles obtained from attitude demodulation at time t, respectively. Neglecting second-order small errors, then and The product is written as: because Therefore, the above equation can be further rewritten as: The above equation can be rewritten as: make The attitude measurement equation is then expressed as: In the formula, Z φ =C φ (1,2), Among them, C φ (1,2) characterizes C φ The element in the first row and second column, C ij (i,j=1,2,3) characterization The element in the i-th row and j-th column.

[0011] Preferably, in step S30, the specific method for integrating the position measurement equation and the attitude measurement equation to obtain the integral measurement equation is as follows: In a short time period, δt = [t] j-1 ,t j Within this range, the misalignment angle error φ is considered to be...n With the position error δp being a constant, integrating the position measurement equation and the attitude measurement equation yields the integral measurement equation: in,

[0012] Preferably, in step S40, the specific method for discretizing the integral measurement equation to obtain the incremental measurement equation is as follows: Discretizing the integral measurement equation, and assuming the IMU and GPS sample N data points in time δt, the incremental measurement equation is written as: in,

[0013] Preferably, in step S40, the Kalman filter is a 40-dimensional linear Kalman filter, and its filter state variable X is represented as: X=[(φ n ) T (δv n ) T (δp) T (X g ) T (X a ) T (δl b ) T φ misz ] T ; in, For speed error; The Kalman filter state equation is expressed as follows: Where F represents the state transition matrix and G represents the system noise driving matrix. Represents the system excitation noise matrix. and These represent the random noise of the gyroscope and the accelerometer, respectively. The state transition matrix F and the system noise driving matrix G are represented as follows: in, This represents the rotation of the n-frame relative to the i-frame; The correlation matrix in the state transition matrix F is represented as follows: F 12 =M2,F 13 =M1+M3, F 23 =(v n ×)(2M1+M3), in, ω represents the projection of the Earth's rotational angular velocity in the n-frame. ie This represents the Earth's angular velocity of rotation; Represents the angular velocity of the n-system. This indicates the navigation solution speed in the n-system; The Kalman filter measurement equation is expressed as follows: Z k =HX+V; in, V represents measurement noise, and H represents the observation transition matrix; The observation transition matrix H is expressed as:

[0014] Preferably, in step S50, the design principles of the aerial calibration and transposition path include: The Y-axis and Z-axis of the IMU are alternately pointed to the sky and the ground through rotational motion; When the aircraft accelerates or decelerates, point the IMU's X-axis toward the aircraft's roll axis; when the aircraft turns, point the IMU's X-axis toward the aircraft's pitch axis. The three sensitive axes of the IMU are rotated at angular velocities of 5° / s to 30° / s respectively; The three sensitive axes of the IMU are alternately pointed to different horizontal directions, and kept still for more than 60 seconds after each rotation.

[0015] Compared with the prior art, the present invention has the following beneficial effects: In a static environment, due to the limitation of the indexing mechanism, the calibration parameters of the outer frame orientation axis type dual-axis RINS accelerometer are... and δK Ax2 The results are not satisfactory; some gyroscope calibration parameters ( and The observability of the data is weak, and previous system-level calibration methods cannot achieve full error parameter calibration of the IMU of the frame-oriented azimuth-axis dual-axis rotating inertial navigation system. The aerial calibration method for the frame-oriented azimuth-axis dual-axis rotating inertial navigation system of this invention can achieve full error parameter calibration of the IMU, thereby achieving the goal of non-disassembly calibration of the frame-oriented azimuth-axis dual-axis RINS in non-laboratory environments, solving the problems of cumbersome calibration and difficult field-level calibration of the frame-oriented azimuth-axis dual-axis rotating inertial navigation system. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, those skilled in the art can obtain other drawings based on the drawings described below without creative effort.

[0017] Figure 1 This is a flowchart illustrating an embodiment of the present invention.

[0018] Figure 2 This is a design diagram of an air calibration and rotation path according to an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this 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 this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. To make the above features and advantages of this invention more apparent and understandable, specific embodiments are provided below with reference to the accompanying drawings for detailed description.

[0020] Example: Figure 1 As shown, an aerial calibration method for an outer frame azimuth-axis dual-axis rotating inertial navigation system includes: S10, IMU calibration error modeling: Define a coordinate system and establish a dual-axis RINS IMU calibration error model based on the coordinate system; S20. Design of the azimuth-position observation method for the moving base: Using GPS position and azimuth information as reference information, the position measurement equation and attitude measurement equation of the moving base are derived, thereby establishing the relationship between the inertial navigation calibration error and the position / azimuth reference information, laying the foundation for the design of the Kalman filter measurement equation in step S40. S30. Measurement equation design based on incremental structure: Integrate the position measurement equation and the attitude measurement equation to obtain the integral measurement equation; Discretize the integral measurement equation to obtain the incremental measurement equation that is easy for computer processing; The incremental measurement equation reduces the impact of GPS position and orientation information measurement noise on the calibration error parameter estimation in step S40. S40. Kalman Filter Design: Based on the IMU calibration error model, design the Kalman filter state equation; based on the incremental measurement equation, design the Kalman filter measurement equation; use the Kalman filter composed of the Kalman filter state equation and the Kalman filter measurement equation to filter and estimate the various IMU calibration error quantities of the dual-axis RINS, and obtain the Kalman filter estimate. S50. Design of airborne calibration and transposition path: Design an airborne calibration and transposition path for the aircraft carrier. The airborne calibration and transposition path is used to fully excite the IMU calibration error and ensure that the Kalman filter estimate converges fully.

[0021] In this embodiment, in step S10, the coordinate system includes the geocentric inertial coordinate system, the Earth coordinate system, the IMU coordinate system, the gyroscope-sensitive coordinate system, the accelerometer-sensitive coordinate system, the aircraft carrier coordinate system, the turntable zero-position coordinate system, the navigation coordinate system, and the navigation calculation coordinate system, respectively denoted as i-system, e-system, b-system, g-system, a-system, m-system, m0-system, n-system, and n′-system, with specific definitions as follows: i series: origin o i Centered on Earth, o i x i and o i y i The axis lies in the plane of the Earth's equator, o i x i The axis points to the vernal equinox, o i z i The axis is the Earth's rotation axis and points towards the North Pole; all inertial device measurement information is based on the i-frame as the reference. e-series: Origin o e Located at the center of the Earth, o e x e The axis lies in the equatorial plane and points towards the central meridian. e z e The axis is along the direction of Earth's rotation, o e x e o e y e and o e z e The relationship between the three axes satisfies the right-hand rule; b series: Origin ob Located in the sensitive center of the IMU, o b x b Axis, o b y b axis and o b z b The axes are respectively aligned with the horizontal axis to the right, the vertical axis forward, and the vertical axis upward, forming a right-front-upper coordinate system; g series: o g x g Axis, o g y g axis and o g z g The axes are respectively aligned with the three gyroscope sensing axes; a series: o a x a Axis, o a y a axis and o a z a The axes are respectively aligned with the sensing axes of the three accelerometers; m-system: Origin o m Located at the sensitive center of the carrier, o m x m Axis, o m y m axis and o m z m The axes are respectively positioned to the right along the horizontal axis of the carrier, forward along the vertical axis, and upward along the vertical axis, forming a right-front-upper coordinate system; m0 system: origin Located at the center of rotation of the turntable, axis, shaft and The axes are respectively aligned to the right along the horizontal axis, forward along the vertical axis, and upward along the vertical axis of the turntable at the zero position, forming a right-front-upper coordinate system; n-system: adopts the Northeast-Heavenly Geographic Coordinate System; n′ system: The northeastern geographic coordinate system calculated using an inertial navigation system.

[0022] The main calibration errors of the IMU include three-axis gyroscope zero bias, three-axis gyroscope scaling error, three-axis gyroscope non-orthogonal error, three-axis accelerometer zero bias, three-axis accelerometer scaling error, three-axis accelerometer non-orthogonal error, three-axis accelerometer quadratic term error coefficient, and three-axis accelerometer inner rod.

[0023] In this embodiment, the IMU calibration error model in step S10 is specifically as follows: in: and δK represents the true angular velocity and measured angular velocity of the three-axis gyroscope, respectively. GThe gyroscope scaling and the gyroscope non-orthogonal error matrix are shown. This indicates that the three-axis gyroscope has zero bias. and δK represents the true specific force and the measured specific force of the triaxial accelerometer, respectively. A For the accelerometer scaling and non-orthogonal error matrix, This indicates that the triaxial accelerometer has zero bias. This indicates the quadratic error of the triaxial accelerometer. This indicates the specific force sensitive to the inner rod of the accelerometer; Let δK be a matrix composed of the squared terms of the accelerometer-sensitive specific force. A2 =[δK Ax2 δK Ay2 δK Az2 ] T The error coefficient for the quadratic term. The error coefficient of the inner lever arm of the accelerometer. This is the inner arm of a triaxial accelerometer; Among them, the gyroscope scale and the gyroscope non-orthogonal error matrix δK G Accelerometer scaling and non-orthogonal error matrix δK A They are represented as follows: Therefore, the measurement error model of the IMU is expressed as: Furthermore, the above formula can be summarized as follows: in:

[0024] In this embodiment, GPS position and attitude information are used as reference information to derive measurement equations based on position and attitude, so as to improve the observability of gyroscope calibration error parameters.

[0025] In this embodiment, the specific method of step S20 includes: S21. In a dynamic environment, first measure and compensate for the lever error between the GPS antenna and the rotation center of the turntable, and then derive the position measurement equation. S22. Using the aircraft base orientation and attitude information provided by the dual-antenna GPS and the relative attitude information provided by the rotation mechanism, the attitude measurement equation is derived.

[0026] In this embodiment, GPS positioning information is a crucial measurement in a dynamic environment. An arm error inevitably exists between the GPS antenna and the turntable's rotation center. Therefore, it is necessary to measure and compensate for this arm error in advance before deriving the position measurement equation. However, relying solely on position information is insufficient for achieving this in a short time. and To address this issue, this invention further utilizes the aircraft base azimuth and attitude information provided by dual-antenna GPS and the relative attitude information provided by the shifting mechanism. By observing the azimuth and attitude of the moving base, it improves... and Observability.

[0027] In this embodiment, in step S21, the position measurement equation is expressed as: In the formula: Where (·×) denotes antisymmetric matrix operation; For the inertial navigation misalignment angle, δp=[δLδλδh] T For positional error, For IMU three-axis external lever arm, The error is represented by the IMU three-axis external boom, where L represents latitude, h represents altitude, and R... M R represents the radius of curvature of the meridional circle. N This represents the radius of curvature of the zonal loop.

[0028] In this embodiment, the derivation process of the attitude measurement equation in step S22 is as follows: For a dual-axis RINS, the demodulated m0-series directional cosine array Represented as: in: In the formula: φ1=[0 Δφ y1 Δφ z1 ] T Let φ2 be the installation error vector between the IMU and the inner frame axis of the indexing mechanism. x2 Δφ y2 0] T This is the installation error vector between the inner frame shaft and the outer frame shaft of the indexing mechanism; Considering the actual If there are errors in north finding and attitude maintenance, then Represented as: therefore, Further expressed as: in: Let φ be the installation error angle between the m-system and the m0-system. mis =[φ misx φ misy φ misz ] T Then the attitude of the aircraft's moving base carrier at time t can be written as: in: According to the matrix chain multiplication rule, the GPS output base attitude... Approximately expressed as: in: in, Let be the azimuth angle output by the GPS at time t. and Let m0 represent the pitch and roll angles obtained from attitude demodulation at time t, respectively. Neglecting second-order small errors, then and The product is written as: because Therefore, the above equation can be further rewritten as: The above equation can be rewritten as: make The attitude measurement equation is then expressed as: In the formula, Z φ =C φ (1,2), Among them, C φ (1,2) characterizes C φ The element in the first row and second column, C ij (i,j=1,2,3) characterization The element in the i-th row and j-th column.

[0029] GPS orientation and positioning information is subject to measurement errors due to atmospheric propagation delay, ephemeris errors, clock errors, SA errors, obstruction, and electromagnetic interference. When GPS orientation errors are large, the accuracy of state estimation during the filtering process is weakened, especially since noise in GPS azimuth measurement information severely affects the accuracy of azimuth and attitude observations. Therefore, this invention employs incremental measurement equations. The incremental structure of these equations can reduce the impact of GPS measurement noise and also reduce the burden of filtering calculations on the navigation computer.

[0030] In this embodiment, the specific method for integrating the position measurement equation and the attitude measurement equation to obtain the integral measurement equation in step S30 is as follows: In a short time period, δt = [t] j-1 ,t j Within this range, the misalignment angle error φ is considered to be... n With the position error δp being a constant, integrating the position measurement equation and the attitude measurement equation yields the integral measurement equation: in,

[0031] In practical applications, inertial navigation systems typically use high-frequency solutions above 100Hz, while GPS outputs low-frequency information of 1Hz or 10Hz. Therefore, the integral measurement equation is not suitable for practical solutions and requires further processing in step S30.

[0032] In this embodiment, the specific method for discretizing the integral measurement equation to obtain the incremental measurement equation in step S30 is as follows: Discretizing the integral measurement equation, and assuming the IMU and GPS sample N data points in time δt, the incremental measurement equation is written as: in,

[0033] In this embodiment, in step S40, the Kalman filter is a 40-dimensional linear Kalman filter. Through Kalman state equation design and Kalman measurement equation design, the filtering estimation of various calibration error parameters of the outer frame orientation axis dual-axis RINS is completed.

[0034] The Kalman filter state variables mainly consist of three parts: (1) navigation error parameters, including misalignment angle error, velocity error and position error; (2) IMU calibration parameters, mainly including three-axis gyroscope zero bias, three-axis gyroscope scale, three-axis gyroscope non-orthogonal error, three-axis accelerometer zero bias, three-axis accelerometer scale, three-axis accelerometer non-orthogonal error, three-axis accelerometer quadratic term error coefficient, and three-axis accelerometer inner lever arm; (3) three-axis outer lever arm error.

[0035] The filter state variable X is represented as: X=[(φ n ) T (δv n ) T (δp) T (X g ) T (X a ) T (δl b ) T φ misz ] T ; in, The remaining variables are defined above and are for speed error. The Kalman filter state equation is expressed as follows: Where F represents the state transition matrix and G represents the system noise driving matrix. Represents the system excitation noise matrix. and These represent the random noise of the gyroscope and the accelerometer, respectively. The state transition matrix F and the system noise driving matrix G are represented as follows: in, This represents the rotation of the n-frame relative to the i-frame; The correlation matrix in the state transition matrix F is represented as follows: F 12 =M2,F 13 =M1+M3, F 23 =(v n ×)(2M1+M3), in, ω represents the projection of the Earth's rotational angular velocity in the n-frame. ie This represents the Earth's angular velocity of rotation; Represents the angular velocity of the n-system. This indicates the navigation solution speed in the n-system; The Kalman filter measurement equation is expressed as follows: Z k =HX+V; in, V represents measurement noise, and H represents the observation transition matrix; The observation transition matrix H is expressed as:

[0036] Step S40 completes the Kalman filter design based on the IMU calibration error model in step S10 and the incremental measurement equation in step S30, providing a tool for the non-disassembly calibration of the frame-oriented dual-axis rotating inertial navigation system. However, it is still necessary to design a reasonable rotation path to fully excite the Kalman filter state variables (i.e., the IMU calibration error variables) and ensure that the various state variables of the filter are fully estimated and converged, thereby solving the problem that previous calibration methods could not achieve full error parameter calibration of the IMU.

[0037] In this embodiment, based on the observability analysis of the IMU calibration error parameters, a suitable rotation path is designed to fully excite all calibration errors of the outer frame azimuth axis dual-axis rotating inertial navigation system (IMU), thereby achieving online system-level calibration of all IMU error parameters.

[0038] In this embodiment, the design principles of the aerial calibration and transposition path in step S50 include: The Y-axis and Z-axis of the IMU are alternately pointed to the sky and the ground through rotational motion; When the aircraft accelerates or decelerates, point the IMU's X-axis toward the aircraft's roll axis; when the aircraft turns, point the IMU's X-axis toward the aircraft's pitch axis. The three sensitive axes of the IMU are rotated at angular velocities of 5° / s to 30° / s respectively; The three sensitive axes of the IMU are alternately pointed to different horizontal directions, and kept still for more than 60 seconds (i.e., ≥1 minute) after each rotation.

[0039] For example, for aircraft carriers, designs are as shown in Table 1 and Figure 2 The rotation path shown consists of 24 rotation stages and takes approximately one hour. It is worth noting that this rotation path is one of the simplest paths that satisfies the full excitation condition of the IMU's total error parameters for the frame-oriented dual-axis rotating inertial navigation system, but it is not the only rotation path. Any rotation path that meets the design principles is acceptable. Table 1: Self-calibration rotation path of a 24-position outer frame azimuth axis dual-axis rotary inertial navigation system

[0040] In a static environment, due to the limitations of the indexing mechanism, the calibration parameters of the outer frame orientation-axis dual-axis RINS accelerometer are limited. and δK Ax2 The results are not satisfactory; some gyroscope calibration parameters ( and The observability of the data is weak, and previous system-level calibration methods cannot achieve full error parameter calibration of the IMU of the frame-oriented azimuth-axis dual-axis rotating inertial navigation system. The aerial calibration method for the frame-oriented azimuth-axis dual-axis rotating inertial navigation system of this invention can achieve full error parameter calibration of the IMU, thereby achieving the goal of non-disassembly calibration of the frame-oriented azimuth-axis dual-axis RINS in non-laboratory environments, solving the problems of cumbersome calibration and difficult field-level calibration of the frame-oriented azimuth-axis dual-axis rotating inertial navigation system.

[0041] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not 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 of the technical features; and these modifications or substitutions do 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 aerial calibration of a frame-oriented dual-axis rotating inertial navigation system, characterized in that, include: S10, IMU calibration error modeling: Define a coordinate system and establish a dual-axis RINS IMU calibration error model based on the coordinate system; S20. Design of the azimuth-position observation method for the moving base: Using GPS position and azimuth information as reference information, the position measurement equation and attitude measurement equation of the moving base are derived, thereby establishing the relationship between the inertial navigation calibration error and the position / azimuth reference information. Specific methods include: S21. In a dynamic environment, first measure and compensate for the lever error between the GPS antenna and the rotation center of the turntable, and then derive the position measurement equation. S22. Using the aircraft base azimuth and attitude information provided by the dual-antenna GPS and the relative attitude information provided by the shifting mechanism, the attitude measurement equation is derived. S30. Measurement equation design based on incremental structure: Integrate the position measurement equation and the attitude measurement equation to obtain an integral measurement equation; Discretize the integral measurement equation to obtain an incremental measurement equation that is easy for computer processing; The incremental measurement equation reduces the influence of GPS position and orientation information measurement noise. S40. Kalman Filter Design: Based on the IMU calibration error model, design the Kalman filter state equation; based on the incremental measurement equation, design the Kalman filter measurement equation; use the Kalman filter composed of the Kalman filter state equation and the Kalman filter measurement equation to filter and estimate the various IMU calibration error quantities of the dual-axis RINS, and obtain the Kalman filter estimate. S50. Design of airborne calibration and transposition path: Design an airborne calibration and transposition path for the aircraft carrier. The airborne calibration and transposition path is used to fully excite the IMU calibration error and ensure that the Kalman filter estimate converges fully.

2. The aerial calibration method for an outer frame azimuth-axis dual-axis rotating inertial navigation system according to claim 1, characterized in that, In step S10, the coordinate systems include the geocentric inertial coordinate system, the Earth coordinate system, the IMU coordinate system, the gyroscope-sensitive coordinate system, the accelerometer-sensitive coordinate system, the aircraft carrier coordinate system, the turntable zero-position coordinate system, the navigation coordinate system, and the navigation calculation coordinate system, which are respectively denoted as... Tie, Tie, Tie, Tie, Tie, Tie, Tie, Tie, The system is specifically defined as follows: Department: origin Centered on Earth and The axis lies in the plane of the Earth's equator. The axis points to the vernal equinox. The axis is the Earth's axis of rotation and points towards the North Pole; Inertial device measurement information is all in This is a reference standard; Department: origin Located at the center of the Earth, The axis lies in the equatorial plane and points towards the central meridian. The axis is along the direction of the Earth's rotation. , and The relationship between the three axes satisfies the right-hand rule; Department: origin Located in the sensitive center of the IMU, axis, shaft and The axes are respectively aligned with the horizontal axis to the right, the vertical axis forward, and the vertical axis upward, forming a right-front-upper coordinate system; Tie: axis, shaft and The axes are respectively aligned with the three gyroscope sensing axes; Tie: axis, shaft and The axes are respectively aligned with the sensing axes of the three accelerometers; Department: origin Located at the sensitive center of the carrier, axis, shaft and The axes are respectively positioned to the right along the horizontal axis of the carrier, forward along the vertical axis, and upward along the vertical axis, forming a right-front-upper coordinate system; Department: origin Located at the center of rotation of the turntable, axis, shaft and The axes are respectively aligned to the right along the horizontal axis, forward along the vertical axis, and upward along the vertical axis of the turntable at the zero position, forming a right-front-upper coordinate system; System: Northeast-Northeast geographic coordinate system; System: The northeastern geographic coordinate system calculated using an inertial navigation system.

3. The aerial calibration method for an outer frame azimuth-axis dual-axis rotating inertial navigation system according to claim 2, characterized in that, In step S10, the IMU calibration error model is specifically as follows: ； in: and These represent the true angular velocity and the measured angular velocity of the three-axis gyroscope, respectively. The gyroscope scaling and the gyroscope non-orthogonal error matrix are shown. This indicates that the three-axis gyroscope has zero bias. and These represent the true specific force and the measured specific force of the triaxial accelerometer, respectively. For the accelerometer scaling and non-orthogonal error matrix, This indicates that the triaxial accelerometer has zero bias. This indicates the quadratic error of the triaxial accelerometer. This indicates the specific force sensitive to the inner rod of the accelerometer; It is a matrix composed of the squared terms of the accelerometer-sensitive specific force. The error coefficient for the quadratic term. The error coefficient of the inner lever arm of the accelerometer. This is the inner arm of a triaxial accelerometer; Among them, the gyroscope scale and the gyroscope non-orthogonal error matrix Accelerometer scaling and non-orthogonal error matrix They are represented as follows: ， ； Therefore, the measurement error model of the IMU is expressed as: ； Furthermore, the above formula can be summarized as follows: ； in: 。 4. The aerial calibration method for an outer frame azimuth-axis dual-axis rotating inertial navigation system according to claim 1, characterized in that, In step S21, the position measurement equation is expressed as: ； In the formula: ， ， ； in, Indicates antisymmetric matrix operations; For the inertial navigation misalignment angle, For positional error, For IMU three-axis external lever arm, For the IMU triaxial external lever error, Indicates latitude, Indicates altitude, This represents the radius of curvature of the meridian. This represents the radius of curvature of the zonal loop.

5. The aerial calibration method for an outer frame azimuth-axis dual-axis rotating inertial navigation system according to claim 4, characterized in that, In step S22, the derivation process of the attitude measurement equation is as follows: For dual-axis RINS, after demodulation System direction cosine array Represented as: ； in: ， ， ， ； In the formula: This is the installation error vector between the IMU and the inner frame axis of the indexing mechanism. This is the installation error vector between the inner frame shaft and the outer frame shaft of the indexing mechanism; Considering the actual If there are errors in north finding and attitude maintenance, then Represented as: ； therefore, Further expressed as: ； in: ； set up System and The installation error angle of the system is Then the attitude of the aircraft's moving base carrier at time t can be written as: ； in: ； According to the matrix chain multiplication rule, the GPS output base attitude... Approximately expressed as: ； in: ， ， ； in, Let be the azimuth angle output by the GPS at time t. and They represent the attitude demodulation results obtained at time t. Pitch angle and roll angle; Neglecting second-order small errors, then and The product is written as: ； because Therefore, the above formula can be further rewritten as: ； The above equation can be rewritten as: ； make The attitude measurement equation is then expressed as: ； In the formula, , ; in, Characterization The element in the first row and second column, Characterization The element in the i-th row and j-th column.

6. The aerial calibration method for an outer frame azimuth-axis dual-axis rotating inertial navigation system according to claim 5, characterized in that, In step S30, the specific method for integrating the position measurement equation and the attitude measurement equation to obtain the integral measurement equation is as follows: In a short period of time Inside, it is considered that the misalignment angle error and position error Assuming the position and attitude measurement equations are constant, integrating them yields the integral measurement equations: ； in, .

7. The aerial calibration method for an outer frame azimuth axis type dual-axis rotating inertial navigation system according to claim 6, characterized in that, In step S30, the specific method for discretizing the integral measurement equation to obtain the incremental measurement equation is as follows: The integral measurement equation is discretized, and the IMU and GPS are assumed to be in... If N data points are sampled within a given time period, the incremental measurement equation can be written as: ； in, .

8. The aerial calibration method for an outer frame azimuth-axis dual-axis rotating inertial navigation system according to claim 7, characterized in that, In step S40, the Kalman filter is a 40-dimensional linear Kalman filter, and its filter state variables... Represented as: ； in, For speed error; The Kalman filter state equation is expressed as follows: ； in, Represents the state transition matrix. Represents the system noise driving matrix. Represents the system excitation noise matrix. and These represent the random noise of the gyroscope and the accelerometer, respectively. State transition matrix and system noise driving matrix They are represented as follows: ； ； in, express System relative to The rotation of the system; State transition matrix The correlation matrix is ​​represented as follows: ， ， ， ， ， ， ， ， ， ， ； in, Indicates the Earth's rotational angular velocity at The projection under the system, This represents the Earth's angular velocity of rotation; express The system is the rotational angular velocity. express Navigation calculation speed under the system; The Kalman filter measurement equation is expressed as follows: ； in, , To measure noise, For observing the transition matrix; Observation transition matrix Represented as: 。 9. The aerial calibration method for a frame-oriented dual-axis rotating inertial navigation system according to claim 1, characterized in that, In step S50, the design principles of the aerial calibration and transposition path include: The Y-axis and Z-axis of the IMU are alternately pointed to the sky and the ground through rotational motion; When the aircraft accelerates or decelerates, point the IMU's X-axis toward the aircraft's roll axis; when the aircraft turns, point the IMU's X-axis toward the aircraft's pitch axis. The three sensitive axes of the IMU are rotated at angular velocities of 5° / s to 30° / s respectively; The three sensitive axes of the IMU are alternately pointed to different horizontal directions, and kept still for more than 60 seconds after each rotation.

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