CN115265590B - Biaxial rotation inertial navigation dynamic error suppression method - Google Patents

Abstract

The invention discloses a method for restraining dynamic errors of biaxial rotation inertial navigation, which comprises the following steps: s1, constructing a coordinate system, and determining an installation error matrix of a gyroscope and an accelerometer; s2, determining an error equation of biaxial rotation inertial navigation under a navigation coordinate system; s3, constructing a thirty-six-dimensional Kalman filter; s4, the double-shaft indexing mechanism rotates according to a designed indexing path, and angular rate data and specific force data in the process are used as calibration data; s5, processing calibration data by using a Kalman filtering algorithm and a Kalman filter to obtain a state quantity estimated value in the Kalman filter; s6, obtaining the angular rate and specific force output after calibration and the acceleration compensated by the rod arm in the accelerometer by using calibration parameters, and further obtaining a navigation result by means of calculation; the method comprehensively considers zero offset, scale factors, installation errors, second-order nonlinear coefficients of the accelerometer and biaxial rotation inertial navigation dynamic errors caused by the inner lever arm of the accelerometer, and has the advantages of simple and convenient application, high precision and good practicability.

Description

Biaxial rotation inertial navigation dynamic error suppression method

Technical Field

The invention relates to the technical field of calibration and inhibition of biaxial rotation inertial navigation errors, in particular to a dynamic error inhibition method of biaxial rotation inertial navigation.

Background

The double-shaft rotation inertial navigation consists of an inertial measurement unit (Initial Measurement Unit, abbreviated as IMU) and an indexing mechanism, and the working principle is as follows: the IMU is arranged on the indexing mechanism, so that the IMU can rotate relative to a fixed coordinate system shaft in the navigation process, and because the IMU modulates constant value errors of an inertial device into periodic variation with zero mean value through specific rotation, the navigation precision of the biaxial rotation inertial navigation long navigation time can be greatly improved on the precision level of the existing inertial device. Accordingly, biaxial rotational inertial navigation is widely used in applications requiring high precision inertial navigation systems, such as: in vessels, warships, airplanes, and the like.

In practical use of biaxial rotation inertial navigation, a reasonable biaxial indexing scheme can completely modulate constant zero offset of inertial devices in an IMU, but cannot modulate dynamic errors caused by carrier motion excitation inertial device scale factor errors, installation errors, accelerometer second-order nonlinear coefficients and accelerometer inner lever arms. Therefore, in order to improve the accuracy of the biaxial rotation inertial navigation in the dynamic environment, it is necessary to accurately calibrate the scale factor error, the installation error, the second-order nonlinear coefficient of the accelerometer and the inner lever arm of the accelerometer of the inertial device of the biaxial rotation inertial navigation, and compensate after calibration to suppress the dynamic error of the biaxial rotation inertial navigation.

To achieve this objective, the disclosed invention patent CN103575296B provides a self-calibration method of a biaxial rotation inertial navigation system, which optimizes a calibration test path by using a genetic algorithm and processes calibration data by using a least square method to calibrate zero offset, scale factors and installation errors of inertial devices in the biaxial rotation inertial navigation IMU; the disclosed invention patent CN104165638B provides a multi-position autonomous calibration method of a biaxial rotation inertial navigation system, which utilizes Kalman filtering and a least square method to calibrate zero offset, scale factors and installation errors of gyroscopes and accelerometers; the published invention patent CN108981751a discloses an eight-position on-line calibration method of a biaxial rotation inertial navigation system, which is used for calibrating zero offset, scale factors and installation errors of an IMU. The existing method can well mark zero offset, scale factors and installation errors of the IMU; however, the two-axis rotation inertial navigation dynamic errors caused by the second-order nonlinear coefficient of the accelerometer and the inner lever arm of the accelerometer are not considered in the scheme, so that the problem that larger errors still exist in the dynamic environment of the two-axis rotation inertial navigation is caused.

Therefore, in order to overcome the problem that the error of the biaxial rotation inertial navigation is large in the dynamic environment due to the fact that the second-order nonlinear coefficient of the accelerometer and the dynamic error of the biaxial rotation inertial navigation caused by the inner lever arm of the accelerometer are not considered in the existing method, a simple, convenient and high-precision method for suppressing the dynamic error of the biaxial rotation inertial navigation is needed to be provided, and zero offset, scale factors, installation errors of the IMU, the second-order nonlinear coefficient of the accelerometer and the inner lever arm of the accelerometer are comprehensively considered.

Disclosure of Invention

The invention aims to provide a biaxial rotation inertial navigation dynamic error restraining method for solving the problem that the error of biaxial rotation inertial navigation under a dynamic environment is larger due to the fact that the second-order nonlinear coefficient of an accelerometer and the dynamic error of the biaxial rotation inertial navigation caused by a lever arm in the accelerometer are not considered in the existing biaxial rotation inertial navigation error calibrating and restraining method.

For this purpose, the technical scheme of the invention is as follows:

A method for restraining dynamic errors of biaxial rotation inertial navigation comprises the following steps:

S1, constructing a gyro sensitive axis system, an accelerometer sensitive axis system, an IMU coordinate system, a geocentric inertial coordinate system, an earth coordinate system and a navigation coordinate system, and determining a gyro installation error matrix and an accelerometer installation error matrix;

s2, determining an error equation of biaxial rotation inertial navigation under a navigation coordinate system based on zero offset, scale factors, installation errors, second-order nonlinear coefficients of an accelerometer and errors caused by a lever arm in the accelerometer of the IMU;

S3, constructing a thirty-six-dimensional Kalman filter based on an error equation of biaxial rotation inertial navigation, wherein the thirty-six-dimensional Kalman filter comprises a state quantity of the thirty-six-dimensional Kalman filter, a state equation of the thirty-six-dimensional Kalman filter, an observation equation of the thirty-six-dimensional Kalman filter and a feedback compensation form of Kalman filter estimation results; wherein the state quantity of the thirty-six-dimensional Kalman filter comprises the attitude error angle of biaxial rotation inertial navigation The method comprises the following steps of speed error delta V, position error delta P, calibration parameter error X _g of a gyroscope, calibration parameter error X _a of an accelerometer, second-order nonlinear coefficient calibration error X _Ka2 of the accelerometer and inner lever arm error X _r;

S4, calibration test: after starting-up preheating is completed, the double-shaft indexing mechanism rotates according to a designed indexing path, and angular rate data output by a gyro and specific force data output by an accelerometer which are subjected to double-shaft rotation inertial navigation in the process are stored to serve as calibration data; wherein, the indexing path should be designed to satisfy: each shaft of the Inertial Measurement Unit (IMU) of the biaxial rotation inertial navigation is subjected to two 180-degree rotations in a single direction, and each shaft of the IMU is subjected to two positions of a finger-to-the-day and a finger-to-ground;

S5, processing the calibration data of the step S4 by using a Kalman filtering algorithm and the Kalman filter constructed in the step S3, so that the state quantity in the Kalman filter is continuously iterated and feedback compensated along with the repeated transposition of the step S4 from an initial value, and finally, the state quantity estimated value in the Kalman filter is obtained; the initial value of the thirty-six-dimensional state quantity is assigned based on the initial alignment result of the biaxial rotation and instrument parameters; in the state quantity estimation value in the optimal Kalman filter, the state quantity component related to the error of the inertial device is a calibration parameter;

S6, substituting the calibration parameters into a calibration model of the gyroscope and a calibration model of the accelerometer to obtain the angular rate and the specific force output after calibration, obtaining the acceleration compensated by the inner lever arm of the accelerometer based on the angular rate and the specific force after calibration, and further obtaining the navigation result of the biaxial rotation inertial navigation after dynamic error real-time compensation through solution.

Further, the specific implementation steps of the step S1 are as follows:

S101, constructing a gyro sensitive axis system, namely a g system, wherein the coordinate system takes measurement center points of three gyroscopes as coordinate origins, xg axes are consistent with the direction of sensitive axes of the X-direction gyroscopes, yg axes are consistent with the direction of sensitive axes of the Y-direction gyroscopes, and Zg axes are consistent with the direction of sensitive axes of the Z-direction gyroscopes;

S102, constructing an accelerometer sensitive axis system, namely an a system, wherein the coordinate system takes a coordinate origin of a g system as a coordinate origin, an Xa axis is consistent with the sensitive axis direction of the X-direction accelerometer, a Ya axis is consistent with the sensitive axis direction of the Y-direction accelerometer, and a Za axis is consistent with the sensitive axis direction of the Z-direction accelerometer;

S103, constructing an IMU coordinate system, namely an m system, wherein the coordinate system takes a coordinate origin of a g system as a coordinate origin, an Xm axis is consistent with an Xg axis of a gyro sensitive axis, a Ym axis is in a plane formed by the Xg axis and the Yg axis of the gyro sensitive axis and is different from the Yg axis by a small angle gamma _yz, and a Zm axis is a small angle gamma _zx of rotation of the Zg axis of the gyro sensitive axis around the Xm axis and then a small angle gamma _zy of rotation around the Ym axis;

s104, constructing a geocentric inertial coordinate system, namely an i system, wherein the coordinate system takes the center of the earth as a coordinate origin, xi and Yi axes are positioned in the equatorial plane of the earth, the Xi axis points to a spring point, and the Zi axis points to the north pole;

S105, constructing an earth coordinate system, namely an e system, wherein the coordinate system takes the center of the earth as a coordinate origin, the Xe and the Ye axes are in the equatorial plane of the earth, the Xe points to the primary meridian, and the Ze axis is the earth rotation axis and points to the north pole;

S106, constructing a navigation coordinate system, namely an n-system, wherein the coordinate system is a northeast geographic coordinate system, the origin of coordinates is the origin of coordinates of an IMU coordinate system, the Xn axis points to the east, the Yn axis points to the north, and the Zn axis points to the sky;

s107, based on a gyro sensitive axis system and an IMU coordinate system, the expression of the installation error matrix of the gyro is as follows:

in the method, in the process of the invention, As installation error matrixes of the gyroscopes, gamma _yz、γ_zy and gamma _zx are three installation error angles of a gyro sensitive axis system relative to an IMU coordinate system, specifically, gamma _yz represents a deflection angle of a Y-direction gyro sensitive axis Yg axis around a Zm axis of an m system, gamma _zy represents a deflection angle of a Z-direction gyro sensitive axis Zg axis around a Ym axis of the m system, and gamma _zx represents a deflection angle of a Z-direction gyro sensitive axis Zg axis around a Xm axis of the m system;

s108, an accelerometer installation error matrix is composed of six accelerometer installation error angles, and the expression is as follows:

in the method, in the process of the invention, As the installation error matrix of the accelerometer, α _xz、α_xy、α_yz、α_yx、α_zy and α _zx are six installation error angles of the accelerometer sensitive axis relative to the IMU coordinate system, specifically, α _xz represents a deflection angle of the X-direction accelerometer sensitive axis Xa about the Zm axis of the m system, α _xy represents a deflection angle of the X-direction accelerometer sensitive axis Xa about the Ym axis of the m system, α _yz represents a deflection angle of the Y-direction accelerometer sensitive axis Ya about the Zm axis of the m system, α _yx represents a deflection angle of the Y-direction accelerometer sensitive axis Ya about the Xm axis of the m system, α _zy represents a deflection angle of the Z-direction accelerometer sensitive axis Za about the Ym axis of the m system, and α _zx represents a deflection angle of the Z-direction accelerometer sensitive axis Za about the Ym axis of the m system.

Further, the specific implementation steps of step S2 are as follows:

The expression of the error equation of the biaxial rotation inertial navigation under the navigation coordinate system (n system) is:

in the method, in the process of the invention, For/>Derivative with respect to time,/>Is the attitude error angle of biaxial rotation inertial navigation,And/>The east error angle, the north error angle and the sky error angle of the biaxial rotation inertial navigation are respectively; /(I)The rotation angle rate of the n system relative to the i system is generated by the rotation of the earth and the movement of a carrier; /(I)To solve for navigationIs determined by the estimation error of (a); /(I)A coordinate conversion matrix from m system to n system; /(I)The measurement error of the gyroscope; /(I)As the derivative of δv ⁿ with respect to time, δv ⁿ is the speed error of biaxial rotational inertial navigation, and δv ⁿ＝[δV_E δV_N δV_U]^T,δV_E、δV_N and δv _U are the east speed error, north speed error and sky speed error, respectively; f ⁿ is the specific force in the n series; /(I)Is the rotation angular rate of the earth; Angular velocity generated for movement of the carrier around the earth; ; v ⁿ is the speed of biaxial rotational inertial navigation, V ⁿ＝[V_E V_N V_U]^T,V_E、V_N and V _U are the east, north and sky speeds of biaxial rotational inertial navigation, respectively; /(I) For/>Error of (2); /(I)For/>Error of (2); δf ^m is the measurement error of the accelerometer; /(I)The error of the rod arm in the accelerometer; δg is a gravity vector error; /(I)Is the derivative of δL with respect to time, δL is the latitude error; /(I)Is the derivative of δλ with respect to time, δλ is the longitude error; /(I)Is the derivative of δh with respect to time, δh is the height error; l, λ and h are local geographic latitude, longitude and altitude, respectively; r _M and R _N are the local earth meridian and mortise meridian radii respectively;

Wherein, the measurement error of the gyro The expression of (2) is: /(I)In the/>Is the measured value of the gyroscope under the m system; δk _G is the error matrix of the scale factor and the installation error of the gyro,

And/>X-direction gyro scale factors/>, respectivelyY-direction gyro scale factor/>And Z-direction gyro scale factor/>Error of (2); δγ _yz、δγ_zy and δγ _zx are errors of gyro mounting error angles γ _yz、γ_zy and γ _zx, respectively; epsilon ^m is zero offset error of the gyro, and the expression is as follows: epsilon ^m＝[ε_x ε_y ε_z]^T, wherein epsilon _x、ε_y and epsilon _z are zero offset errors of an X-direction gyroscope, a Y-direction gyroscope and a Z-direction gyroscope respectively;

the measurement error δf ^m of the accelerometer is expressed as: in the/> Is a measurement value of the accelerometer under the m system; δk _A is the error matrix of the scale factor and the mounting error of the accelerometer,And/>Scale factors/>, respectively, for X-direction accelerometersY-direction accelerometer scale factor/>And Z-direction accelerometer scale factor/>Error of (2); δα _xz、δα_xy、δα_yz、δα_yx、δα_zy and δα _zx are the errors of accelerometer mounting error angles α _xz、α_xy、α_yz、α_yx、α_zy and α _zx, respectively; δK _A2 is a calibration error matrix of the second order nonlinear coefficient of the accelerometer,/>Δk _ax2、δK_ay2 and δk _az2 are the calibration error of the second-order nonlinear coefficient K _ax2 of the X-direction accelerometer, the calibration error of the second-order nonlinear coefficient K _ay2 of the Y-direction accelerometer, and the calibration error of the second-order nonlinear coefficient K _az2 of the Z-direction accelerometer, respectively; /(I)As the zero offset error of the accelerometer,And/>Zero offset errors of the X-direction accelerometer, the Y-direction accelerometer and the Z-direction accelerometer respectively;

Accelerometer inner lever arm error The expression of (2) is: /(I)In the/> And/>Inner boom error/>, respectivelyComponents on the X _m axis, Y _m axis and Z _m axis in the m-system,Wherein,And/>Measured value/>, respectively, of the gyroscope in the m-systemComponents on the X _m axis, Y _m axis, and Z _m axis; δr _x、δr_y and δr _z are the errors of the X-direction accelerometer inner lever arm r _x, the Y-direction accelerometer inner lever arm r _y and the Z-direction accelerometer inner lever arm r _z, respectively.

Further, the specific implementation steps of step S3 are as follows:

s301, constructing a state quantity X ³⁶ of a thirty-six-dimensional Kalman filter:

wherein, in the formula, Is the attitude error angle of biaxial rotation inertial navigation,/>Δv is the velocity error, δv= [ δv _E δV_N δV_U]^T; δp is a position error, δp= [ δlδλδh ] ^T;X_g is a calibration parameter error of the gyro,X _a is the calibration parameter error of the accelerometer,X _Ka2 is the second-order nonlinear coefficient calibration error of the accelerometer, X _Ka2＝[δK_ax2 δK_ay2 δK_az2]^T;X_r is the inner lever arm error, X _r＝[δr_x δr_y δr_z]^T;

S302, constructing a state equation of a thirty-six-dimensional Kalman filter:

in the method, in the process of the invention, In the case of F ³³, the process is carried out,

In the case of F ³⁶, the following components,

G ³⁶ is the measurement noise input matrix as,U is measurement noise,/>Wherein u _g is the measurement noise of the gyroscope, and u _a is the measurement noise of the accelerometer;

S303, constructing an observation equation of a thirty-six-dimensional Kalman filter: z=h ³⁶X³⁶ +v,

Wherein Z is observed quantity, the speed is observed quantity, and the biaxial rotation inertial navigation is kept in a static state during calibration, Z= [ V _E V_N V_U]^T;H³⁶ ] is an observation matrix, and H ³⁶＝[0_3×3 I₃ 0_3×30],I₃ is a unit matrix of three rows and three columns, namely0 _3×30 Is a zero matrix of three rows and thirty columns, and 0 _3×3 is a zero matrix of three rows and three columns; v is observation noise;

s304, determining a feedback compensation form of a Kalman filtering estimation result:

in the method, in the process of the invention, For/>Is an antisymmetric matrix of/>Is biaxial rotation inertial navigation/>Is a result of the solution; /(I)The solution result of V ⁿ which is biaxial rotation inertial navigation; /(I)The solution result of L is biaxial rotation inertial navigation; /(I)The result of the solution of lambda for biaxial rotation inertial navigation; /(I)The solution result of h is biaxial rotation inertial navigation; (v)/(v)Feeding back K _G before compensation for the Kalman filtering estimation result; /(I)Epsilon ^m before feeding back compensation for Kalman filtering estimation results; (v)/(v)Feeding back K _A before compensation for the Kalman filtering estimation result; /(I)Feedback of the estimation result for Kalman filtering before compensationFeeding back K _A2 before compensation for the Kalman filtering estimation result; /(I)Feeding back r _x before compensation for the Kalman filtering estimation result; /(I)Feeding back r _y before compensation for the Kalman filtering estimation result; /(I)And feeding back r _z before compensation for the Kalman filtering estimation result.

Further, in step S4, the indexing path of the biaxial indexing mechanism is specifically designed as:

corresponding initial positions based on order 0: biaxial rotation inertial navigation is carried out in a posture that the Xm axis of the biaxial rotation inertial navigation faces east, the Ym axis faces north and the Zm axis faces sky, and the biaxial rotation inertial navigation is static for 10 minutes;

order 1: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of the biaxial rotation inertial navigation is oriented east, the Ym axis is oriented upward, and the Zm axis is oriented south; after the transposition is completed, standing for 180s;

Order 2: the middle frame shaft is taken as a rotating shaft and rotates clockwise for 180 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented east, the Ym axis is oriented earth, and the Zm axis is oriented north; after the transposition is completed, standing for 180s;

Order 3: the middle frame shaft is taken as a rotating shaft and rotates clockwise for 180 degrees; in this state, the Xm axis of the biaxial rotation inertial navigation is oriented east, the Ym axis is oriented upward, and the Zm axis is oriented south; after the transposition is completed, standing for 180s;

Order 4: the inner frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented upward, the Ym axis is oriented western, and the Zm axis is oriented southward; after the transposition is completed, standing for 180s;

Order 5: the inner frame shaft is taken as a rotating shaft and rotates clockwise for 180 degrees; in this state, the Xm axis of the biaxial rotational inertial navigation is oriented, the Ym axis is oriented east, and the Zm axis is oriented south; after the transposition is completed, standing for 180s;

Order 6: the inner frame shaft is taken as a rotating shaft and rotates clockwise for 180 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented upward, the Ym axis is oriented western, and the Zm axis is oriented southward; after the transposition is completed, standing for 180s;

Order 7: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of the biaxial rotational inertial navigation is oriented in the south direction, the Ym axis is oriented in the west direction, and the Zm axis is oriented in the ground; after the transposition is completed, standing for 180s;

Order 8: the middle frame shaft is taken as a rotating shaft and rotates clockwise for 180 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented north, the Ym axis is oriented west, and the Zm axis is oriented sky; after the transposition is completed, standing for 180s;

Order 9: the middle frame shaft is taken as a rotating shaft and rotates clockwise for 180 degrees; in this state, the Xm axis of the biaxial rotational inertial navigation is oriented in the south direction, the Ym axis is oriented in the west direction, and the Zm axis is oriented in the ground; after the transposition is completed, standing for 180s;

Sequence 10: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented, the Ym axis is oriented in the west direction, and the Zm axis is oriented in the north direction; after the transposition is completed, standing for 180s;

order 11: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented north, the Ym axis is oriented west, and the Zm axis is oriented sky; after the transposition is completed, standing for 180s;

Order 12: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented upward, the Ym axis is oriented western, and the Zm axis is oriented southward; after the transposition is completed, standing for 180s;

Order 13: the inner frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented in the western direction, the Ym axis is oriented in the ground, and the Zm axis is oriented in the south direction; after the transposition is completed, standing for 180s;

sequence 14: the inner frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of the biaxial rotational inertial navigation is oriented, the Ym axis is oriented east, and the Zm axis is oriented south; after the transposition is completed, standing for 180s;

order 15: the inner frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of the biaxial rotation inertial navigation is oriented east, the Ym axis is oriented upward, and the Zm axis is oriented south; after the transposition is completed, standing for 180s;

Order 16: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of the biaxial rotational inertial navigation is oriented east, the Ym axis is oriented south, and the Zm axis is oriented earth; after the transposition is completed, standing for 180s;

order 17: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented east, the Ym axis is oriented earth, and the Zm axis is oriented north; after the transposition is completed, standing for 180s;

Order 18: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented east, the Ym axis is oriented north, and the Zm axis is oriented sky; after the indexing is completed, the machine is stationary for 180s.

Further, in step S4, indexing of the biaxial indexing mechanism is performed 1 to 3 times according to the designed indexing path in one calibration experiment.

Further, the specific implementation steps of step S5 are as follows:

S501, carrying out initial value assignment on thirty-six-dimensional state quantity: and the initial value of delta V is respectively assigned by the initial attitude angle and the initial speed in the initial alignment result of the biaxial rotation in the step S4; the initial value of delta P is assigned by subtracting the actual experimental position from the initial position output after the initial alignment is completed by biaxial rotation inertial navigation in the step S4; the initial values of X _g、X_a、X_Ka2 and X _r are assigned according to the actual conditions of the gyroscope and the accelerometer in the biaxial rotation inertial navigation;

S502, based on the thirty-six-dimensional state quantity initial value determined in the step S501 as the initial value of the Kalman filtering state quantity, bringing the thirty-six-dimensional state quantity constructed in the step S301 into the thirty-six-dimensional Kalman filter state equation constructed in the step S302 and the thirty-six-dimensional Kalman filter observation equation constructed in the step S303 respectively, adopting a Kalman filtering algorithm and the Kalman filter constructed in the step S3 to process calibration data, and continuously iterating and feeding back the state quantity in the Kalman filter from the initial value to compensate to obtain the state quantity estimated value in the Kalman filter; the state quantity component related to the error of the inertial device in the state quantity estimation value is an accurate calibration parameter, which comprises the following steps: x-direction gyro scale factor Y-direction gyro scale factor/>And Z-direction gyro scale factor/>Gyro mounting error angles gamma _yz、γ_zy and gamma _zx; zero bias of X-direction gyroY-direction gyro zero offsetAnd Z-direction gyro zero bias/>X-direction accelerometer scale factor/>Y-direction accelerometer scale factor/>And Z-direction accelerometer scale factor/>Error of (2); accelerometer mounting error angles α _xz、α_xy、α_yz、α_yx、α_zy and α _zx; a second order nonlinear coefficient K _ax2 of the X-direction accelerometer, a second order nonlinear coefficient K _ay2 of the Y-direction accelerometer and a second order nonlinear coefficient K _az2 of the Z-direction accelerometer; zero bias of X-direction accelerometerY-direction accelerometer zero bias/>And Z-direction accelerometer zero bias/>X-direction accelerometer inner lever arm r _x, Y-direction accelerometer inner lever arm r _y, and Z-direction accelerometer inner lever arm r _z;

further, the specific implementation steps of step S6 are as follows:

S601, adopting the existing sixty-four order rotation modulation scheme as an indexing mechanism rotation scheme in the biaxial rotation inertial navigation process, stopping for 10S after rotating to one position each time, and obtaining an inertial device output result after rotation modulation, including the angular rate of gyro output And accelerometer output specific force/>

S602, substituting the calibration parameters obtained in the step S5 into a gyro calibration model and an accelerometer calibration model respectively to obtain output after gyro calibration and output after accelerometer calibration; wherein,

(1) The calibrating model of the gyroscope is as follows:

in the method, in the process of the invention,

(2) The calibration model of the accelerometer is as follows:

in the method, in the process of the invention,

S603, using the output after gyro calibration and the output after accelerometer calibration obtained in the step S602, using the X-direction accelerometer inner lever arm r _x, the Y-direction accelerometer inner lever arm r _y and the Z-direction accelerometer inner lever arm r _z to compensate acceleration data in real time, wherein the specific formula is as follows:

Wherein a _xb、a_yb and a _zb are components of an Xm axis, a Ym axis and a Zm axis in an m system of acceleration real-time results after the compensation of a lever arm in the accelerometer; a _xc、a_yc and a _zc are components of the acceleration real-time result before the compensation of the rod arm in the accelerometer, namely an Xm axis, a Ym axis and a Zm axis in an m system; omega _xc、ω_yc and omega _zc are components of the angular rate in the m-system of the Xm-axis, the Ym-axis and the Zm-axis;

S604, bringing a _xb、a_yb、a_zb and omega _xc、ω_yc、ω_zc in the step S603 into an inertial navigation solution equation to obtain a navigation result of biaxial rotation inertial navigation, namely, a navigation result obtained by carrying out real-time compensation on dynamic errors of biaxial rotation inertial navigation by adopting the method.

Compared with the prior art, the double-shaft rotation inertial navigation dynamic error suppression method has the beneficial effects that:

(1) The method for restraining the dynamic error of the biaxial rotation inertial navigation is simple and convenient and has high precision, and comprehensively considers zero offset, scale factors, installation errors, second-order nonlinear coefficients of the accelerometer and dynamic errors of the biaxial rotation inertial navigation caused by the inner lever arm of the accelerometer of the IMU;

(2) After calibration and compensation are carried out by adopting the method provided by the application, the speed error caused by dynamic is obviously reduced, the effect can reach 90%, the positioning accuracy of the biaxial rotation inertial navigation in a dynamic environment can be improved by about 8 meters, and the correctness and the accuracy of the method provided by the application are proved, so that the dynamic error of the biaxial rotation inertial navigation can be well restrained, and the practicability is good.

Drawings

FIG. 1 is a schematic flow chart of a method for suppressing dynamic errors in biaxial rotation inertial navigation according to the present invention;

FIG. 2 is a schematic diagram of the coordinate system conversion between the gyro sensitive axis system and the IMU coordinate system constructed in step S1 of the present invention;

FIG. 3 (a) is a schematic diagram of the comparison of east velocity errors before and after dynamic error compensation of biaxial rotational inertial navigation according to an embodiment of the present invention;

FIG. 3 (b) is a schematic diagram showing the comparison of the north velocity errors before and after the dynamic error compensation of the biaxial rotation inertial navigation according to the embodiment of the present invention;

FIG. 4 (a) is a schematic diagram of the comparison of the east position errors of the biaxial rotational inertial navigation before and after the dynamic error compensation according to the embodiment of the present invention;

fig. 4 (b) is a schematic diagram of comparison of north position errors before and after dynamic error compensation in the biaxial rotation inertial navigation according to the embodiment of the present invention.

Detailed Description

The invention will now be further described with reference to the accompanying drawings and specific examples, which are in no way limiting.

As shown in fig. 1, the specific implementation steps of the method for suppressing the dynamic error of the biaxial rotation inertial navigation are as follows:

s1, constructing a gyro sensitive axis system (g system), an accelerometer sensitive axis system (a system), an IMU coordinate system (m system), a geocentric inertial coordinate system (i system), an earth coordinate system (e system) and a navigation coordinate system (n system), and determining a gyro installation error matrix and an accelerometer installation error matrix;

specifically, in this step S1, the coordinate system is constructed as follows:

(1) The gyro sensitive axis system, also called g system for short, is expressed as: o-XgYgZg; the coordinate system takes the measurement center points of the three gyroscopes as coordinate origins (o points), the Xg axis of the coordinate system is consistent with the direction of the sensitive axis of the X-direction gyroscopes, the Yg axis of the coordinate system is consistent with the direction of the sensitive axis of the Y-direction gyroscopes, and the Zg axis of the coordinate system is consistent with the direction of the sensitive axis of the Z-direction gyroscopes; because in the IMU of biaxial rotation inertial navigation, the three gyroscopes cannot guarantee strict orthogonal installation, and therefore, the g system is not an orthogonal coordinate system;

(2) The accelerometer sensitive axis system, also called a system for short, is expressed as: o-XaYaZa; the coordinate origin of the coordinate system is coincident with the coordinate origin of the g system, namely the coordinate origin (o point) of the g system is taken as the coordinate origin, the Xa axis is coincident with the sensitive axis direction of the X-direction accelerometer, the Ya axis is coincident with the sensitive axis direction of the Y-direction accelerometer, and the Za axis is coincident with the sensitive axis direction of the Z-direction accelerometer; likewise, because in an IMU of biaxial rotational inertial navigation, three accelerometers cannot be mounted rigidly orthogonally, nor is the a-system an orthogonal coordinate system;

(3) The IMU coordinate system, also called m system for short, is expressed as: o-XmYmZm; since inertial navigation solution requires the projection of the output of each inertial device into the same orthogonal coordinate system, the coordinate system is an orthogonal coordinate system for projecting the outputs of the gyroscopes and accelerometers as orthogonal vectors; as shown in fig. 2, the origin of coordinates of the coordinate system coincides with the origin of coordinates of the g system, that is, the origin of coordinates (o-point) of the g system is taken as the origin of coordinates, the Xm axis coincides with the gyro sensitive axis Xg axis, the Ym axis is in a plane formed by the gyro sensitive axis Xg axis and the Yg axis and is different from the Yg axis by a small angle gamma _yz, the Zm axis is the gyro sensitive axis Zg axis rotating around the Xm axis by a small angle gamma _zx, and then rotating around the Ym axis by a small angle gamma _zy;

(4) The geocentric inertial coordinate system, also called i system for short, is represented as o _e -XiYiZi, which is used as a reference standard for the output of an inertial device, the origin o _e of the coordinate is the center of the earth, the Xi and Yi axes are in the equatorial plane of the earth, the Xi axis points to the vernal division point (i.e. one of the intersection points of the equatorial plane and then the celestial sphere), and the Zi axis is the earth rotation axis and points to the north pole;

(5) The earth coordinate system, also called the e system for short, is denoted as o _e -XeYeZe; the origin o _e of the coordinate system is the center of the earth, the Xe and the Ye axes are in the equatorial plane of the earth, the Xe points to the original meridian, and the Ze axis is the rotation axis of the earth and points to the north pole; the earth coordinate system is fixedly connected with the earth, and the angular velocity of the e system relative to the i system is the earth rotation angular velocity;

(6) A navigation coordinate system, also called n system for short, which is denoted as o-XnYnZn; the coordinate system is used as a coordinate system adopted by inertial navigation in solving navigation parameters, in particular to a northeast geographic coordinate system, the origin o of the coordinate is the origin of coordinates of an IMU coordinate system, the Xn axis points to the east, the Yn axis points to the north, the Zn axis points to the sky, and the azimuth relation of the n system relative to the e system is the geographic position of the carrier;

Based on the gyroscope sensitive axis system (g system) and the IMU coordinate system (m system) constructed above, the expression of the installation error matrix of the gyroscope can be determined as follows:

in the method, in the process of the invention, As installation error matrixes of the gyroscopes, gamma _yz、γ_zy and gamma _zx are three installation error angles of a gyro sensitive axis system relative to an IMU coordinate system, specifically, gamma _yz represents a deflection angle of a Y-direction gyro sensitive axis Yg axis around a Zm axis of an m system, gamma _zy represents a deflection angle of a Z-direction gyro sensitive axis Zg axis around a Ym axis of the m system, and gamma _zx represents a deflection angle of a Z-direction gyro sensitive axis Zg axis around a Xm axis of the m system;

In addition, because of the small angle installation error between the gyro component and the accelerometer component, in order to convert the measurement information of the accelerometer into the IMU coordinate system, the installation error matrix of the accelerometer is composed of six accelerometer installation error angles, and the expression is as follows:

in the method, in the process of the invention, As an installation error matrix of the accelerometer, alpha _xz、α_xy、α_yz、α_yx、α_zy and alpha _zx are six installation error angles of an accelerometer sensitive axis relative to an IMU coordinate system, specifically, alpha _xz represents a deflection angle of an X-direction accelerometer sensitive axis Xa around an m-axis Zm-axis, alpha _xy represents a deflection angle of an X-direction accelerometer sensitive axis Xa around an m-axis Ym-axis, alpha _yz represents a deflection angle of a Y-direction accelerometer sensitive axis Ya around an m-axis Zm-axis, alpha _yx represents a deflection angle of a Y-direction accelerometer sensitive axis Ya around an m-axis Xm-axis, alpha _zy represents a deflection angle of a Z-direction accelerometer sensitive axis Za around an m-axis Zm-axis, and alpha _zx represents a deflection angle of a Z-direction accelerometer sensitive axis Za around an m-axis Xm-axis;

S2, determining an error equation of biaxial rotation inertial navigation under a navigation coordinate system (n system) based on zero offset, scale factors, installation errors, second-order nonlinear coefficients of an accelerometer and errors caused by a lever arm in the accelerometer of the IMU, wherein the expression is as follows:

/>

in the method, in the process of the invention, For/>Derivative with respect to time,/>Is the attitude error angle of biaxial rotation inertial navigation,And/>The east error angle, the north error angle and the sky error angle of the biaxial rotation inertial navigation are respectively; /(I)The rotation angle rate of the n system relative to the i system is generated by the rotation of the earth and the movement of a carrier; /(I)To solve for navigationIs determined by the estimation error of (a); /(I)A coordinate conversion matrix from m system to n system; /(I)The measurement error of the gyroscope; /(I)As the derivative of δv ⁿ with respect to time, δv ⁿ is the speed error of biaxial rotational inertial navigation, and δv ⁿ＝[δV_E δV_N δV_U]^T,δV_E、δV_N and δv _U are the east speed error, north speed error and sky speed error, respectively; f ⁿ is the specific force in the n series; /(I)Is the rotation angular rate of the earth; Angular velocity generated for movement of the carrier around the earth; ; v ⁿ is the speed of biaxial rotational inertial navigation, V ⁿ＝[V_E V_N V_U]^T,V_E、V_N and V _U are the east, north and sky speeds of biaxial rotational inertial navigation, respectively; /(I) For/>Error of (2); /(I)For/>Error of (2); δf ^m is the measurement error of the accelerometer; /(I)The error of the rod arm in the accelerometer; δg is a gravity vector error; /(I)Is the derivative of δL with respect to time, δL is the latitude error; /(I)Is the derivative of δλ with respect to time, δλ is the longitude error; /(I)Is the derivative of δh with respect to time, δh is the height error; l, λ and h are local geographic latitude, longitude and altitude, respectively; r _M and R _N are the local earth meridian and mortise meridian radii respectively;

Wherein, the measurement error of the gyro The expression of (2) is: /(I)

In the method, in the process of the invention,Is the measured value of the gyroscope under the m system; δK _G is the error matrix of the scale factor and installation error of the gyro,/>And/>Respectively X-direction gyro scale factorsY-direction gyro scale factor/>And Z-direction gyro scale factor/>Error of (2); δγ _yz、δγ_zy and δγ _zx are errors of gyro mounting error angles γ _yz、γ_zy and γ _zx, respectively;

Epsilon ^m is zero offset error of the gyro, and the expression is as follows: epsilon ^m＝[ε_x ε_y ε_z]^T of the total number of the components,

Wherein epsilon _x、ε_y and epsilon _z are zero offset errors of an X-direction gyroscope, a Y-direction gyroscope and a Z-direction gyroscope respectively;

the measurement error δf ^m of the accelerometer is expressed as:

in the method, in the process of the invention, Is a measurement value of the accelerometer under the m system; δK _A is the error matrix of the scale factor and mounting error of the accelerometer,/>And/>Scale factors/>, respectively, for X-direction accelerometersY-direction accelerometer scale factor/>And Z-direction accelerometer scale factor/>Error of (2); δα _xz、δα_xy、δα_yz、δα_yx、δα_zy and δα _zx are the errors of accelerometer mounting error angles α _xz、α_xy、α_yz、α_yx、α_zy and α _zx, respectively; δK _A2 is a calibration error matrix of the second order nonlinear coefficient of the accelerometer,/>Δk _ax2、δK_ay2 and δk _az2 are the calibration error of the second-order nonlinear coefficient K _ax2 of the X-direction accelerometer, the calibration error of the second-order nonlinear coefficient K _ay2 of the Y-direction accelerometer, and the calibration error of the second-order nonlinear coefficient K _az2 of the Z-direction accelerometer, respectively; /(I)Is zero offset error of accelerometer,/>And/>Zero offset errors of the X-direction accelerometer, the Y-direction accelerometer and the Z-direction accelerometer respectively;

Accelerometer inner lever arm error The expression of (2) is: /(I)

In the method, in the process of the invention,And/>Inner boom error/>, respectivelyComponents on the X _m axis, Y _m axis and Z _m axis in m-line,/> Wherein/>And/>Measured value/>, respectively, of the gyroscope in the m-systemComponents on the X _m axis, Y _m axis, and Z _m axis; δr _x、δr_y and δr _z are the errors of the X-direction accelerometer inner lever arm r _x, the Y-direction accelerometer inner lever arm r _y and the Z-direction accelerometer inner lever arm r _z, respectively;

s3, constructing a thirty-six-dimensional Kalman filter based on the error equation of the biaxial rotation inertial navigation determined in the step S2, wherein the implementation steps are as follows:

S301, constructing a state quantity X ³⁶ of a thirty-six-dimensional Kalman filter, wherein the state quantity X ³⁶ is as follows:

in the method, in the process of the invention, Is the attitude error angle of biaxial rotation inertial navigation,/>Δv is the velocity error, δv= [ δv _E δV_N δV_U]^T; δp is a position error, δp= [ δlδλδh ] ^T;X_g is a calibration parameter error of the gyro,X _a is the calibration parameter error of the accelerometer,X _Ka2 is the second-order nonlinear coefficient calibration error of the accelerometer, X _Ka2＝[δK_ax2 δK_ay2 δK_az2]^T;X_r is the inner lever arm error, X _r＝[δr_x δr_y δr_z]^T;

S302, constructing a state equation of a thirty-six-dimensional Kalman filter:

in the method, in the process of the invention, Wherein, in F ³³, each non-zero matrix element is: /(I)

/>

In the case of F ³⁶, the following components,

G ³⁶ is the measurement noise input matrix as,U is measurement noise,/>Wherein u _g is the measurement noise of the gyroscope, and u _a is the measurement noise of the accelerometer;

s303, constructing an observation equation of a thirty-six-dimensional Kalman filter, wherein the observation equation is as follows:

Z＝H³⁶X³⁶+v，

wherein Z is observed quantity, the speed is observed quantity, and the biaxial rotation inertial navigation is kept in a static state during calibration, Z= [ V _E V_N V_U]^T;H³⁶ ] is an observation matrix, and H ³⁶＝[0_3×3 I₃ 0_3×30],I₃ is a unit matrix of three rows and three columns, namely 0 _3×30 Is a zero matrix of three rows and thirty columns, and 0 _3×3 is a zero matrix of three rows and three columns; v is observation noise;

s304, determining a feedback compensation form of a Kalman filtering estimation result:

in the method, in the process of the invention, For/>Is an antisymmetric matrix of/>Is biaxial rotation inertial navigation/>Is a result of the solution; /(I)The solution result of V ⁿ which is biaxial rotation inertial navigation; /(I)The solution result of L is biaxial rotation inertial navigation; /(I)The result of the solution of lambda for biaxial rotation inertial navigation; /(I)The solution result of h is biaxial rotation inertial navigation; (v)/(v)Feeding back K _G before compensation for the Kalman filtering estimation result; /(I)Epsilon ^m before feeding back compensation for Kalman filtering estimation results; (v)/(v)Feeding back K _A before compensation for the Kalman filtering estimation result; /(I)Feedback of the estimation result for Kalman filtering before compensationFeeding back K _A2 before compensation for the Kalman filtering estimation result; /(I)Feeding back r _x before compensation for the Kalman filtering estimation result; /(I)Feeding back r _y before compensation for the Kalman filtering estimation result; /(I)Feeding back r _z before compensation for the Kalman filtering estimation result;

s4, designing an indexing path of the double-shaft indexing mechanism in a calibration test and performing the calibration test;

The specific steps of the step S4 are as follows:

S401, designing an indexing path of a double-shaft indexing mechanism in a calibration test;

the double-shaft indexing mechanism of the double-shaft rotary inertial navigation system comprises a middle frame shaft and an inner frame shaft which are mutually perpendicular and in the same plane; the rotation of the middle frame shaft and the inner frame shaft is controlled to control the indexing path of the double-shaft indexing mechanism, so that the IMU coordinate system continuously changes the gesture; setting the rotating speed of the double-shaft indexing mechanism to be 5 degrees/s; the index paths are shown in table 1 below, specifically:

Order 0: the biaxial indexing mechanism is at an initial position, wherein the frame shaft faces east, the inner frame shaft faces upward, and correspondingly, the Xm shaft of biaxial rotation inertial navigation faces east, the Ym shaft faces north and the Zm shaft faces upward; the biaxial indexing mechanism is initially stationary for 10 minutes, so that biaxial rotation inertial navigation is initially aligned in the stationary process, an initial navigation resolving result comprising an attitude angle and a speed is obtained, and then the navigation resolving state is entered;

Order 1: the middle frame shaft is taken as a rotating shaft, the middle frame shaft rotates 90 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 1, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis faces east, the Ym axis faces up, and the Zm axis faces south; and rest for 180s at the rotated position of sequence 1;

order 2: the middle frame shaft is taken as a rotating shaft, the middle frame shaft rotates 180 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 2, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis faces east, the Ym axis faces earth, and the Zm axis faces north; and is stationary for 180s at the rotated position of sequence 2;

Order 3: the middle frame shaft is taken as a rotating shaft, the middle frame shaft rotates 180 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 3, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis faces east, the Ym axis faces up, and the Zm axis faces south; and is stationary for 180s at the rotated position of sequence 3;

Order 4: the inner frame shaft is taken as a rotating shaft, the inner frame shaft rotates 90 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 4, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis faces upward, the Ym axis faces west, and the Zm axis faces south; and is stationary for 180s at the rotated position of sequence 4;

Order 5: the inner frame shaft is taken as a rotating shaft, the inner frame shaft rotates 180 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 5, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis is oriented to the ground, the Ym axis is oriented to the east, and the Zm axis is oriented to the south; and is stationary for 180s at the rotated position of sequence 5;

Order 6: the inner frame shaft is taken as a rotating shaft, the inner frame shaft rotates 180 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 6, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis faces upward, the Ym axis faces west, and the Zm axis faces south; and is stationary for 180s at the rotated position of sequence 6;

order 7: the middle frame shaft is taken as a rotating shaft, the middle frame shaft rotates 90 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 7, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis is oriented in the south direction, the Ym axis is oriented in the west direction, and the Zm axis is oriented in the ground direction; and is stationary for 180s at the rotated position of sequence 7;

Order 8: the middle frame shaft is taken as a rotating shaft, the middle frame shaft rotates 180 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 8, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis faces north, the Ym axis faces west, and the Zm axis faces sky; and is stationary for 180s at the rotated position of sequence 8;

Order 9: the middle frame shaft is taken as a rotating shaft, the middle frame shaft rotates 180 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 9, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis is oriented in the south direction, the Ym axis is oriented in the west direction, and the Zm axis is oriented in the ground direction; and is stationary for 180s at the rotated position of sequence 9;

Sequence 10: the middle frame shaft is taken as a rotating shaft, the middle frame shaft rotates 90 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 10, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis is oriented to the ground, the Ym axis is oriented to the west, and the Zm axis is oriented to the north; and is stationary for 180s at the rotated sequence 10 position;

Order 11: the middle frame shaft is taken as a rotation shaft, the rotation shaft rotates 90 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 11, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis faces north, the Ym axis faces west, and the Zm axis faces sky; and is stationary for 180s at the rotated position of sequence 11;

Order 12: the middle frame shaft is taken as a rotation shaft, the rotation shaft rotates 90 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 12, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis faces upward, the Ym axis faces west, and the Zm axis faces south; and is stationary for 180s at the rotated position of sequence 12;

order 13: the inner frame shaft is taken as a rotation shaft, the rotation shaft rotates 90 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 13, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis is oriented to the west, the Ym axis is oriented to the ground, and the Zm axis is oriented to the south; and is stationary for 180s at the rotated position of sequence 13;

sequence 14: the inner frame shaft is taken as a rotation shaft, the rotation shaft rotates 90 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 14, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis is oriented to the ground, the Ym axis is oriented to the east, and the Zm axis is oriented to the south; and is stationary for 180s at the rotated position of sequence 14;

order 15: the inner frame shaft is taken as a rotating shaft, the inner frame shaft rotates 90 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 15, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis faces east, the Ym axis faces up, and the Zm axis faces south; and is stationary for 180s at the rotated position of sequence 15;

order 16: the middle frame shaft is taken as a rotation shaft, the rotation shaft rotates 90 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 16, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis faces east, the Ym axis faces south, and the Zm axis faces earth; and is stationary for 180s at the rotated position of sequence 16;

order 17: the middle frame shaft is taken as a rotating shaft, the middle frame shaft rotates 90 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 17, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis faces east, the Ym axis faces earth, and the Zm axis faces north; and is stationary for 180s at the rotated position of sequence 17;

order 18: the middle frame shaft is taken as a rotation shaft, the rotation shaft rotates 90 degrees clockwise, the rotated indexing mechanism gesture is recorded as a sequence 18, and the specific gesture corresponding to the biaxial rotation inertial navigation is as follows: the Xm axis faces east, the Ym axis faces north, and the Zm axis faces sky; and is stationary for 180s at the rotated positions of sequence 18;

Table 1:

the whole indexing process involves 18 times of sequence turning, and the whole indexing path can be completed within 1 hour after the whole indexing process stops 180s after each time of turning to a designated position;

In the above indexing path, the first nine turns (order 1-9) aim to excite gyro scale factor errors and installation errors, thus comprising two 180 ° rotations for each axis of the IMU in a single direction; the purpose of the last nine turns (order 10-18) is to excite accelerometer scale factors and mounting errors, thus encompassing two positions of the fingery and fingery of each axis of the IMU; meanwhile, the calibration path can also meet the excitation and decoupling of the second-order nonlinear coefficient of the accelerometer; in actual calibration, the random noise of the gyroscope is relatively large, and the estimation of the zero offset error of the gyroscope in the Kalman filter usually needs a relatively long time, so that the calibration path transposition is carried out twice in one calibration, the complete convergence of the estimation curve of each calibration parameter error can be ensured, and the state quantity estimation value in the Kalman filter is finally obtained; ;

s402, preheating at least four hours after starting up to reduce the influence of temperature change on calibration;

S403, finishing a calibration experiment, namely controlling the rotation of the double-shaft indexing mechanism according to a calibration indexing path designed in the step S401, and storing angular rate data output by a gyroscope and specific force data output by an accelerometer as calibration data;

S5, processing the calibration data obtained in the step S4 by utilizing the Kalman filter constructed in the step S3 to obtain calibration parameters, wherein the specific implementation process is as follows:

S501, giving an initial value of thirty-six-dimensional state quantity in the thirty-six-dimensional Kalman filter, namely giving Is the initial value of (2); wherein,

And δv= [ δv _E δV_N δV_U]^T, wherein the initial value is directly assigned by the initial attitude angle and the initial speed in the initial alignment result of the biaxial rotation, specifically: the initial value of the gesture obtained after the initial alignment of the biaxial rotation inertial navigation is carried out by the indexing mechanism which is stationary for 10 minutes in the initial state in the step S4: /(I)And initial value of velocity: v ₀＝[V_E0 V_N0 V_U0]^T as/>And an initial value of δV, i.e., in the initial state,/>δV＝V₀；

The initial value of delta P is assigned by subtracting the actual laboratory position from the initial position output after the initial alignment is completed by the biaxial rotation inertial navigation in the step S4, and specifically comprises the following steps: 1) The position of the laboratory is obtained by using a GPS to be P _t＝[L_t λ_t h_t]^T, wherein L _t、λ_t and h _t are the latitude, longitude and altitude of the laboratory respectively; 2) S4, outputting an initial position P ₀＝[L₀ λ₀ h₀]^T after initial alignment is completed by biaxial rotation inertial navigation; 3) The initial value of δP is set as: [ L ₀-L_t λ₀-λ_t h₀-h_t]^T;

The initial values of X _g、X_a、X_Ka2 and X _r are assigned according to the actual conditions of the gyroscope and the accelerometer used by the specific biaxial rotation inertial navigation (namely, the initial values are determined after artificial consideration is carried out through the type of the instrument, the precision level and the mechanical structure design characteristics);

S502, based on the thirty-six-dimensional state quantity initial value determined in the step S501 as the initial value of the Kalman filtering state quantity, bringing the thirty-six-dimensional state quantity constructed in the step S301 into the thirty-six-dimensional Kalman filter state equation constructed in the step S302 and the thirty-six-dimensional Kalman filter observation equation constructed in the step S303, and processing calibration data by using a Kalman filtering algorithm and the Kalman filter constructed in the step S3, so that the state quantity in the Kalman filter is continuously iterated and feedback compensated along with the repeated transposition of the step S4 from the initial value, wherein the feedback compensation adopts a feedback compensation mode of the estimation result determined in the step S304, and finally the state quantity estimation value in the Kalman filter is obtained;

in the state quantity estimation value, the state quantity component related to the error of the inertial device is the accurate calibration parameter obtained through step S5, which includes: x-direction gyro scale factor Y-direction gyro scale factor/>And Z-direction gyro scale factorGyro mounting error angles gamma _yz、γ_zy and gamma _zx; zero bias of X-direction gyroY-direction gyro zero bias/>Zero offset of Z-direction gyroX-direction accelerometer scale factor/>Y-direction accelerometer scale factor/>And Z-direction accelerometer scale factor/>Error of (2); accelerometer mounting error angles α _xz、α_xy、α_yz、α_yx、α_zy and α _zx; a second order nonlinear coefficient K _ax2 of the X-direction accelerometer, a second order nonlinear coefficient K _ay2 of the Y-direction accelerometer and a second order nonlinear coefficient K _az2 of the Z-direction accelerometer; zero offset of X-direction accelerometerY-direction accelerometer zero bias/>And Z-direction accelerometer zero bias/>An X-direction accelerometer inner lever arm r _x, a Y-direction accelerometer inner lever arm r _y, and a Z-direction accelerometer inner lever arm r _z;

S6, substituting the calibration parameters into a calibration model to compensate the output of the biaxial rotation inertial navigation; the specific implementation steps are as follows:

s601, adopting a common indexing mechanism rotation scheme (such as a sixty four-order rotation modulation scheme) as an indexing mechanism rotation scheme in the biaxial rotation inertial navigation process, stopping for 10S after rotating to one position, and obtaining an inertial device output result after rotation modulation, including the angular rate of gyro output And accelerometer output specific force/>

In step S603, the sixty-four order rotation modulation scheme is a known indexing scheme for use in biaxial rotation inertial navigation, that is, an indexing scheme when navigation is performed by mounting on a carrier, and therefore will not be described in detail in this embodiment;

s602, substituting the calibration parameters obtained in the step S5 into a gyro calibration model and an accelerometer calibration model respectively to obtain output after gyro calibration and output after accelerometer calibration; wherein,

(1) The calibrating model of the gyroscope is as follows:/>

in the method, in the process of the invention,

(2) The calibration model of the accelerometer is as follows:

in the method, in the process of the invention,

S603, using the output after gyro calibration and the output after accelerometer calibration obtained in the step S602, using the X-direction accelerometer inner lever arm r _x, the Y-direction accelerometer inner lever arm r _y and the Z-direction accelerometer inner lever arm r _z to compensate acceleration data in real time, wherein the specific formula is as follows:

Wherein a _xb、a_yb and a _zb are components of an Xm axis, a Ym axis and a Zm axis in an m system of acceleration real-time results after the compensation of a lever arm in the accelerometer; a _xc、a_yc and a _zc are components of an acceleration real-time result f ^m before the compensation of a lever arm in the accelerometer, an Xm axis, a Ym axis and a Zm axis in an m system; omega _xc、ω_yc and omega _zc are angular rates Components of Xm axis, ym axis and Zm axis in m-system;

S604, introducing a _xb、a_yb、a_zb, omega _xc、ω_yc and omega _zc in the step S603 into an inertial navigation solution equation to obtain a navigation result of biaxial rotation inertial navigation;

the navigation result obtained in step S604 is the navigation result obtained by compensating the dynamic error of biaxial rotation inertial navigation in real time by adopting the method.

In order to verify the correctness and accuracy of the dynamic error suppression method of the biaxial rotation inertial navigation provided by the invention, a set of biaxial rotation inertial navigation is selected for calibration experiments, and the IMU in the selected biaxial rotation inertial navigation consists of three laser gyroscopes with zero offset stability of 0.01 degrees/h and three accelerometers with zero offset stability of 10 mug; the attitude control precision of the selected indexing mechanism of the biaxial rotation inertial navigation is 5' (1 sigma).

Firstly, the method provided by the invention is adopted to calibrate error parameters, and initial values of X _g、X_a、X_Ka2 and X _r in X ³⁶ are determined according to the selected types and precision levels of gyroscopes and accelerometers used in biaxial rotation inertial navigation and mechanical structure design as follows: x-direction gyro scale factorY-direction gyro scale factor/>And Z-direction gyro scale factor/>The initial values of (2) are-0.84'/pulse; the initial values of the gyro installation error angles gamma _yz、γ_zy and gamma _zx are 10'; zero bias of X-direction gyroY-direction gyro zero bias/>And Z-direction gyro zero bias/>The initial values of (2) are all 0.01 DEG/h; x-direction accelerometer scale factor/>Y-direction accelerometer scale factor/>And Z-direction accelerometer scale factor/>The initial values of (2) are all 450 μm/s/pulse; the initial values of the accelerometer installation error angles alpha _xz、α_xy、α_yz、α_yx、α_zy and alpha _zx are 10'; the initial values of the second-order nonlinear coefficient K _ax2 of the X-direction accelerometer, the second-order nonlinear coefficient K _ay2 of the Y-direction accelerometer and the second-order nonlinear coefficient K _az2 of the Z-direction accelerometer are 20 mug/g 2; zero bias of X-direction accelerometerY-direction accelerometer zero bias/>And Z-direction accelerometer zero bias/>The initial values of (2) are 1000 mug; the initial values of the X-direction accelerometer inner lever arm r _x, the Y-direction accelerometer inner lever arm r _y and the Z-direction accelerometer inner lever arm r _z are 3cm;

the calibration parameters obtained according to the set initial value and the method provided by the invention are as follows:

Table 2:

after the calibration parameters are obtained, mounting the selected biaxial inertial navigation on a test vehicle to carry out vehicle-mounted dynamic experiments, wherein the experiments comprise 10-minute static initial alignment and 10-minute navigation calculation, firstly, carrying out 10-minute static initial alignment under the condition that the test vehicle is carried out, entering a navigation state after the alignment is finished, starting to linearly start a simulated dynamic environment at a speed of 15m/s, turning the test vehicle by 180 degrees after the biaxial rotational inertial navigation enters the navigation state for about 4 minutes, and continuing to linearly start at the speed of 15m/s after turning; after the navigation state is performed for about 8 minutes, the test vehicle turns 180 degrees again, and the rotation directions are the same for the two times.

The method comprises the steps of performing navigation calculation on the same set of experimental data by respectively adopting a calibration method which does not consider the secondary nonlinear parameters of the accelerometer and the errors of the lever arm in the accelerometer and two sets of parameters of the method provided by the invention, and comparing the navigation calculation result with the speed and the position of GPS output arranged on a test vehicle.

FIG. 3 (a) is a schematic diagram showing the east velocity error contrast of biaxial rotational inertial navigation before and after dynamic error compensation; FIG. 3 (b) is a schematic diagram showing the comparison of the north velocity errors before and after the dynamic error compensation by the biaxial rotation inertial navigation. As can be seen from the comparison of the two graphs, under the condition that the secondary nonlinear parameter of the accelerometer and the rod arm error in the accelerometer are not compensated, the 180-degree steering of the biaxial rotation inertial navigation can generate about 0.025m/s of speed error in the east direction and the north direction, and the speed error caused by dynamic state is obviously reduced after the calibration and compensation are carried out by adopting the method provided by the invention, and the effect can reach 90%;

FIG. 4 (a) is a schematic diagram showing the comparison of the east position errors before and after dynamic error compensation by biaxial rotation inertial navigation; FIG. 4 (b) is a schematic diagram showing the comparison of the north position errors before and after the dynamic error compensation by the biaxial rotation inertial navigation. As can be seen from the comparison of the two graphs, the two non-linear parameters of the accelerometer, the rod arm error in the accelerometer and the position error of the navigation result obtained by the method can be compared, and the positioning accuracy of biaxial rotation inertial navigation in a dynamic environment can be improved by about 8 meters in a navigation environment with short navigation time.

In conclusion, the experiment proves the correctness and the accuracy of the method for restraining the dynamic error of the biaxial rotation inertial navigation, which is provided by the invention, has the effect of being capable of restraining the dynamic error of the biaxial rotation inertial navigation well, and has good practicability.

The invention, in part, is not disclosed in detail and is well known in the art. While the foregoing describes illustrative embodiments of the present invention to facilitate an understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, but is to be construed as protected by all the inventions by the appended claims insofar as such variations are within the spirit and scope of the present invention as defined and defined by the appended claims.

Claims (8)

1. The method for restraining the dynamic error of the biaxial rotation inertial navigation is characterized by comprising the following steps:

S1, constructing a gyro sensitive axis system, an accelerometer sensitive axis system, an IMU coordinate system, a geocentric inertial coordinate system, an earth coordinate system and a navigation coordinate system, and determining a gyro installation error matrix and an accelerometer installation error matrix;

s2, determining an error equation of biaxial rotation inertial navigation under a navigation coordinate system based on zero offset, scale factors, installation errors, second-order nonlinear coefficients of an accelerometer and errors caused by a lever arm in the accelerometer of the IMU;

S3, constructing a thirty-six-dimensional Kalman filter based on an error equation of biaxial rotation inertial navigation, wherein the thirty-six-dimensional Kalman filter comprises a state quantity of the thirty-six-dimensional Kalman filter, a state equation of the thirty-six-dimensional Kalman filter, an observation equation of the thirty-six-dimensional Kalman filter and a feedback compensation form of Kalman filter estimation results; wherein the state quantity of the thirty-six-dimensional Kalman filter comprises the attitude error angle of biaxial rotation inertial navigation The method comprises the following steps of speed error delta V, position error delta P, calibration parameter error X _g of a gyroscope, calibration parameter error X _a of an accelerometer, second-order nonlinear coefficient calibration error X _Ka2 of the accelerometer and inner lever arm error X _r;

S4, calibration test: after starting-up preheating is completed, the double-shaft indexing mechanism rotates according to a designed indexing path, and angular rate data output by a gyro and specific force data output by an accelerometer which are subjected to double-shaft rotation inertial navigation in the process are stored to serve as calibration data; wherein, the indexing path should be designed to satisfy: each shaft of the biaxial rotation inertial measurement unit rotates 180 degrees twice in a unidirectional direction, and each shaft of the inertial measurement unit passes through two positions of a finger-to-the-day position and a finger-to-ground position;

S5, processing the calibration data of the step S4 by using a Kalman filtering algorithm and the Kalman filter constructed in the step S3, so that the state quantity in the Kalman filter is continuously iterated and feedback compensated along with the repeated transposition of the step S4 from an initial value, and finally, the state quantity estimated value in the Kalman filter is obtained; the initial value of the thirty-six-dimensional state quantity is assigned based on the initial alignment result of the biaxial rotation and instrument parameters; in the state quantity estimation value in the optimal Kalman filter, the state quantity component related to the error of the inertial device is a calibration parameter;

S6, substituting the calibration parameters into a calibration model of the gyroscope and a calibration model of the accelerometer to obtain the angular rate and the specific force output after calibration, obtaining the acceleration compensated by the inner lever arm of the accelerometer based on the angular rate and the specific force after calibration, and further obtaining the navigation result of the biaxial rotation inertial navigation after dynamic error real-time compensation through solution.

2. The method for suppressing dynamic errors in biaxial rotation inertial navigation according to claim 1, wherein the implementation step of step S1 is as follows:

S101, constructing a gyro sensitive axis system, namely a g system, wherein the coordinate system takes measurement center points of three gyroscopes as coordinate origins, xg axes are consistent with the direction of sensitive axes of the X-direction gyroscopes, yg axes are consistent with the direction of sensitive axes of the Y-direction gyroscopes, and Zg axes are consistent with the direction of sensitive axes of the Z-direction gyroscopes;

S102, constructing an accelerometer sensitive axis system, namely an a system, wherein the coordinate system takes a coordinate origin of a g system as a coordinate origin, an Xa axis is consistent with the sensitive axis direction of the X-direction accelerometer, a Ya axis is consistent with the sensitive axis direction of the Y-direction accelerometer, and a Za axis is consistent with the sensitive axis direction of the Z-direction accelerometer;

S103, constructing an IMU coordinate system, namely an m system, wherein the coordinate system takes a coordinate origin of a g system as a coordinate origin, an Xm axis is consistent with an Xg axis of a gyro sensitive axis, a Ym axis is in a plane formed by the Xg axis and the Yg axis of the gyro sensitive axis and is different from the Yg axis by a small angle gamma _yz, and a Zm axis is a small angle gamma _zx of rotation of the Zg axis of the gyro sensitive axis around the Xm axis and then a small angle gamma _zy of rotation around the Ym axis;

s104, constructing a geocentric inertial coordinate system, namely an i system, wherein the coordinate system takes the center of the earth as a coordinate origin, xi and Yi axes are positioned in the equatorial plane of the earth, the Xi axis points to a spring point, and the Zi axis points to the north pole;

S105, constructing an earth coordinate system, namely an e system, wherein the coordinate system takes the center of the earth as a coordinate origin, the Xe and the Ye axes are in the equatorial plane of the earth, the Xe points to the primary meridian, and the Ze axis is the earth rotation axis and points to the north pole;

S106, constructing a navigation coordinate system, namely an n-system, wherein the coordinate system is a northeast geographic coordinate system, the origin of coordinates is the origin of coordinates of an IMU coordinate system, the Xn axis points to the east, the Yn axis points to the north, and the Zn axis points to the sky;

s107, based on a gyro sensitive axis system and an IMU coordinate system, the expression of the installation error matrix of the gyro is as follows:

in the method, in the process of the invention, As installation error matrixes of the gyroscopes, gamma _yz、γ_zy and gamma _zx are three installation error angles of a gyro sensitive axis system relative to an IMU coordinate system, specifically, gamma _yz represents a deflection angle of a Y-direction gyro sensitive axis Yg axis around a Zm axis of an m system, gamma _zy represents a deflection angle of a Z-direction gyro sensitive axis Zg axis around a Ym axis of the m system, and gamma _zx represents a deflection angle of a Z-direction gyro sensitive axis Zg axis around a Xm axis of the m system;

s108, an accelerometer installation error matrix is composed of six accelerometer installation error angles, and the expression is as follows:

in the method, in the process of the invention, As the installation error matrix of the accelerometer, α _xz、α_xy、α_yz、α_yx、α_zy and α _zx are six installation error angles of the accelerometer sensitive axis relative to the IMU coordinate system, specifically, α _xz represents a deflection angle of the X-direction accelerometer sensitive axis Xa about the Zm axis of the m system, α _xy represents a deflection angle of the X-direction accelerometer sensitive axis Xa about the Ym axis of the m system, α _yz represents a deflection angle of the Y-direction accelerometer sensitive axis Ya about the Zm axis of the m system, α _yx represents a deflection angle of the Y-direction accelerometer sensitive axis Ya about the Xm axis of the m system, α _zy represents a deflection angle of the Z-direction accelerometer sensitive axis Za about the Ym axis of the m system, and α _zx represents a deflection angle of the Z-direction accelerometer sensitive axis Za about the Ym axis of the m system.

3. The method for suppressing dynamic errors in biaxial rotation inertial navigation according to claim 2, wherein the implementation step of step S2 is as follows:

The expression of the error equation of the biaxial rotation inertial navigation under the navigation coordinate system is as follows:

in the method, in the process of the invention, For/>Derivative with respect to time,/>Is the attitude error angle of biaxial rotation inertial navigation,/> And/>The east error angle, the north error angle and the sky error angle of the biaxial rotation inertial navigation are respectively; /(I)The rotation angle rate of the n system relative to the i system is generated by the rotation of the earth and the movement of a carrier; /(I)To solve for navigationIs determined by the estimation error of (a); a coordinate conversion matrix from m system to n system; /(I) The measurement error of the gyroscope; /(I)As the derivative of δv ⁿ with respect to time, δv ⁿ is the speed error of biaxial rotational inertial navigation, and δv ⁿ＝[δV_E δV_N δV_U]^T,δV_E、δV_N and δv _U are the east speed error, north speed error and sky speed error, respectively; f ⁿ is the specific force in the n series; /(I)Is the rotation angular rate of the earth; /(I)Angular velocity generated for movement of the carrier around the earth; ; v ⁿ is the speed of biaxial rotational inertial navigation, V ⁿ＝[V_E V_N V_U]^T,V_E、V_N and V _U are the east, north and sky speeds of biaxial rotational inertial navigation, respectively; /(I)For/>Error of (2); /(I)For/>Error of (2); δf ^m is the measurement error of the accelerometer; /(I)The error of the rod arm in the accelerometer; δg is a gravity vector error; /(I)Is the derivative of δL with respect to time, δL is the latitude error; /(I)Is the derivative of δλ with respect to time, δλ is the longitude error; /(I)Is the derivative of δh with respect to time, δh is the height error; l, λ and h are local geographic latitude, longitude and altitude, respectively; r _M and R _N are the local earth meridian and mortise meridian radii respectively;

Wherein, the measurement error of the gyro The expression of (2) is:

in the method, in the process of the invention, Is the measured value of the gyroscope under the m system; δk _G is the error matrix of the scale factor and the installation error of the gyro, And/>X-direction gyro scale factors/>, respectivelyY-direction gyro scale factor/>And Z-direction gyro scale factor/>Error of (2); δγ _yz、δγ_zy and δγ _zx are errors of gyro mounting error angles γ _yz、γ_zy and γ _zx, respectively;

Epsilon ^m is zero offset error of the gyro, and the expression is as follows:

ε^m＝[ε_x ε_y ε_z]^T，

Wherein epsilon _x、ε_y and epsilon _z are zero offset errors of an X-direction gyroscope, a Y-direction gyroscope and a Z-direction gyroscope respectively;

the measurement error δf ^m of the accelerometer is expressed as:

in the method, in the process of the invention, Is a measurement value of the accelerometer under the m system; δK _A is the error matrix of the scale factor and mounting error of the accelerometer,/> And/>Scale factors/>, respectively, for X-direction accelerometersY-direction accelerometer scale factor/>And Z-direction accelerometer scale factor/>Error of (2); δα _xz、δα_xy、δα_yz、δα_yx、δα_zy and δα _zx are the errors of accelerometer mounting error angles α _xz、α_xy、α_yz、α_yx、α_zy and α _zx, respectively; δK _A2 is a calibration error matrix of the second order nonlinear coefficient of the accelerometer,/>Δk _ax2、δK_ay2 and δk _az2 are the calibration error of the second-order nonlinear coefficient K _ax2 of the X-direction accelerometer, the calibration error of the second-order nonlinear coefficient K _ay2 of the Y-direction accelerometer, and the calibration error of the second-order nonlinear coefficient K _az2 of the Z-direction accelerometer, respectively; /(I)As the zero offset error of the accelerometer, And/>Zero offset errors of the X-direction accelerometer, the Y-direction accelerometer and the Z-direction accelerometer respectively;

Accelerometer inner lever arm error The expression of (2) is:

in the method, in the process of the invention, And/>Inner boom error/>, respectivelyComponents on the X _m axis, Y _m axis and Z _m axis in the m-system, Wherein/>And/>Measured value/>, respectively, of the gyroscope in the m-systemComponents on the X _m axis, Y _m axis, and Z _m axis; δr _x、δr_y and δr _z are the errors of the X-direction accelerometer inner lever arm r _x, the Y-direction accelerometer inner lever arm r _y and the Z-direction accelerometer inner lever arm r _z, respectively.

4. The method for suppressing dynamic errors in biaxial rotation inertial navigation according to claim 3, wherein the implementation step of step S3 is as follows:

s301, constructing a state quantity X ³⁶ of a thirty-six-dimensional Kalman filter:

wherein, in the formula, Is the attitude error angle of biaxial rotation inertial navigation,/>Δv is the velocity error, δv= [ δv _E δV_N δV_U]^T; δp is a position error, δp= [ δlδλδh ] ^T;X_g is a calibration parameter error of the gyro,X _a is the calibration parameter error of the accelerometer,X _Ka2 is the second-order nonlinear coefficient calibration error of the accelerometer, X _Ka2＝[δK_ax2 δK_ay2 δK_az2]^T;X_r is the inner lever arm error, X _r＝[δr_x δr_y δr_z]^T;

S302, constructing a state equation of a thirty-six-dimensional Kalman filter:

in the method, in the process of the invention, In F ³³, each non-zero matrix element is:

In the case of F ³⁶, the following components,

G ³⁶ is the measurement noise input matrix as,U is measurement noise,/>Wherein u _g is the measurement noise of the gyroscope, and u _a is the measurement noise of the accelerometer;

S303, constructing an observation equation of a thirty-six-dimensional Kalman filter:

Z＝H³⁶X³⁶+v，

Wherein Z is observed quantity, the speed is observed quantity, and the biaxial rotation inertial navigation is kept in a static state during calibration, Z= [ V _EV_N V_U]^T;H³⁶ ] is an observation matrix, and H ³⁶＝[0_3×3 I₃ 0_3×30],I₃ is a unit matrix of three rows and three columns, namely 0 _3×30 Is a zero matrix of three rows and thirty columns, and 0 _3×3 is a zero matrix of three rows and three columns; v is observation noise;

s304, determining a feedback compensation form of a Kalman filtering estimation result:

in the method, in the process of the invention, For/>Is an antisymmetric matrix of/>Is biaxial rotation inertial navigation/>Is a result of the solution; /(I)The solution result of V ⁿ which is biaxial rotation inertial navigation; /(I)The solution result of L is biaxial rotation inertial navigation; /(I)The result of the solution of lambda for biaxial rotation inertial navigation; /(I)The solution result of h is biaxial rotation inertial navigation; (v)/(v)Feeding back K _G before compensation for the Kalman filtering estimation result; /(I)Epsilon ^m before feeding back compensation for Kalman filtering estimation results; (v)/(v)Feeding back K _A before compensation for the Kalman filtering estimation result; /(I)Feedback of the estimation result for Kalman filtering before compensation Feeding back K _A2 before compensation for the Kalman filtering estimation result; /(I)Feeding back r _x before compensation for the Kalman filtering estimation result; /(I)Feeding back r _y before compensation for the Kalman filtering estimation result; /(I)And feeding back r _z before compensation for the Kalman filtering estimation result.

5. The method of claim 1, wherein in step S4, the indexing path of the biaxial indexing mechanism is specifically designed as follows:

corresponding initial positions based on order 0: biaxial rotation inertial navigation is carried out in a posture that the Xm axis of the biaxial rotation inertial navigation faces east, the Ym axis faces north and the Zm axis faces sky, and the biaxial rotation inertial navigation is static for 10 minutes;

order 1: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of the biaxial rotation inertial navigation is oriented east, the Ym axis is oriented upward, and the Zm axis is oriented south; after the transposition is completed, standing for 180s;

Order 2: the middle frame shaft is taken as a rotating shaft and rotates clockwise for 180 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented east, the Ym axis is oriented earth, and the Zm axis is oriented north; after the transposition is completed, standing for 180s;

Order 3: the middle frame shaft is taken as a rotating shaft and rotates clockwise for 180 degrees; in this state, the Xm axis of the biaxial rotation inertial navigation is oriented east, the Ym axis is oriented upward, and the Zm axis is oriented south; after the transposition is completed, standing for 180s;

Order 4: the inner frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented upward, the Ym axis is oriented western, and the Zm axis is oriented southward; after the transposition is completed, standing for 180s;

Order 5: the inner frame shaft is taken as a rotating shaft and rotates clockwise for 180 degrees; in this state, the Xm axis of the biaxial rotational inertial navigation is oriented, the Ym axis is oriented east, and the Zm axis is oriented south; after the transposition is completed, standing for 180s;

Order 6: the inner frame shaft is taken as a rotating shaft and rotates clockwise for 180 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented upward, the Ym axis is oriented western, and the Zm axis is oriented southward; after the transposition is completed, standing for 180s;

Order 7: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of the biaxial rotational inertial navigation is oriented in the south direction, the Ym axis is oriented in the west direction, and the Zm axis is oriented in the ground; after the transposition is completed, standing for 180s;

Order 8: the middle frame shaft is taken as a rotating shaft and rotates clockwise for 180 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented north, the Ym axis is oriented west, and the Zm axis is oriented sky; after the transposition is completed, standing for 180s;

Order 9: the middle frame shaft is taken as a rotating shaft and rotates clockwise for 180 degrees; in this state, the Xm axis of the biaxial rotational inertial navigation is oriented in the south direction, the Ym axis is oriented in the west direction, and the Zm axis is oriented in the ground; after the transposition is completed, standing for 180s;

Sequence 10: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented, the Ym axis is oriented in the west direction, and the Zm axis is oriented in the north direction; after the transposition is completed, standing for 180s;

order 11: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented north, the Ym axis is oriented west, and the Zm axis is oriented sky; after the transposition is completed, standing for 180s;

Order 12: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented upward, the Ym axis is oriented western, and the Zm axis is oriented southward; after the transposition is completed, standing for 180s;

Order 13: the inner frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented in the western direction, the Ym axis is oriented in the ground, and the Zm axis is oriented in the south direction; after the transposition is completed, standing for 180s;

sequence 14: the inner frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of the biaxial rotational inertial navigation is oriented, the Ym axis is oriented east, and the Zm axis is oriented south; after the transposition is completed, standing for 180s;

order 15: the inner frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of the biaxial rotation inertial navigation is oriented east, the Ym axis is oriented upward, and the Zm axis is oriented south; after the transposition is completed, standing for 180s;

Order 16: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of the biaxial rotational inertial navigation is oriented east, the Ym axis is oriented south, and the Zm axis is oriented earth; after the transposition is completed, standing for 180s;

order 17: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented east, the Ym axis is oriented earth, and the Zm axis is oriented north; after the transposition is completed, standing for 180s;

Order 18: the middle frame shaft is taken as a rotating shaft and rotates clockwise by 90 degrees; in this state, the Xm axis of biaxial rotational inertial navigation is oriented east, the Ym axis is oriented north, and the Zm axis is oriented sky; after the indexing is completed, the machine is stationary for 180s.

6. The method of claim 5, wherein in step S4, indexing of the biaxial rotation inertial navigation dynamic error mechanism is performed twice according to the designed indexing path in one calibration experiment.

7. The method for suppressing dynamic error of biaxial rotation inertial navigation according to claim 3, wherein the implementation step of step S5 is as follows:

S501, carrying out initial value assignment on thirty-six-dimensional state quantity: and the initial value of delta V is respectively assigned by the initial attitude angle and the initial speed in the initial alignment result of the biaxial rotation in the step S4; the initial value of delta P is assigned by subtracting the actual experimental position from the initial position output after the initial alignment is completed by biaxial rotation inertial navigation in the step S4; the initial values of X _g、X_a、X_Ka2 and X _r are assigned according to the actual conditions of the gyroscope and the accelerometer in the biaxial rotation inertial navigation;

S502, based on the thirty-six-dimensional state quantity initial value determined in the step S501 as the initial value of the Kalman filtering state quantity, bringing the thirty-six-dimensional state quantity constructed in the step S301 into the thirty-six-dimensional Kalman filter state equation constructed in the step S302 and the thirty-six-dimensional Kalman filter observation equation constructed in the step S303 respectively, adopting a Kalman filtering algorithm and the Kalman filter constructed in the step S3 to process calibration data, and continuously iterating and feeding back the state quantity in the Kalman filter from the initial value to compensate to obtain the state quantity estimated value in the Kalman filter; the state quantity component related to the error of the inertial device in the state quantity estimation value is an accurate calibration parameter, which comprises the following steps: x-direction gyro scale factor Y-direction gyro scale factor/>And Z-direction gyro scale factor/>Gyro mounting error angles gamma _yz、γ_zy and gamma _zx; zero bias of X-direction gyroY-direction gyro zero bias/>And Z-direction gyro zero bias/>X-direction accelerometer scale factor/>Y-direction accelerometer scale factor/>And Z-direction accelerometer scale factor/>Error of (2); accelerometer mounting error angles α _xz、α_xy、α_yz、α_yx、α_zy and α _zx; a second order nonlinear coefficient K _ax2 of the X-direction accelerometer, a second order nonlinear coefficient K _ay2 of the Y-direction accelerometer and a second order nonlinear coefficient K _az2 of the Z-direction accelerometer; zero bias of X-direction accelerometerY-direction accelerometer zero bias/>And Z-direction accelerometer zero bias/>X-direction accelerometer inner lever arm r _x, Y-direction accelerometer inner lever arm r _y, and Z-direction accelerometer inner lever arm r _z.

8. The method for suppressing dynamic errors in biaxial rotation inertial navigation according to claim 7, wherein the implementation step of step S6 is as follows:

S601, adopting the existing sixty-four order rotation modulation scheme as an indexing mechanism rotation scheme in the biaxial rotation inertial navigation process, stopping for 10S after rotating to one position each time, and obtaining an inertial device output result after rotation modulation, including the angular rate of gyro output And accelerometer output specific force/>

S602, substituting the calibration parameters obtained in the step S5 into a gyro calibration model and an accelerometer calibration model respectively to obtain output after gyro calibration and output after accelerometer calibration; wherein,

(1) The calibrating model of the gyroscope is as follows:

in the method, in the process of the invention,

(2) The calibration model of the accelerometer is as follows:

in the method, in the process of the invention,

S603, using the output after gyro calibration and the output after accelerometer calibration obtained in the step S602, using the X-direction accelerometer inner lever arm r _x, the Y-direction accelerometer inner lever arm r _y and the Z-direction accelerometer inner lever arm r _z to compensate acceleration data in real time, wherein the specific formula is as follows:

Wherein a _xb、a_yb and a _zb are components of an Xm axis, a Ym axis and a Zm axis in an m system of acceleration real-time results after the compensation of a lever arm in the accelerometer; a _xc、a_yc and a _zc are components of the acceleration real-time result before the compensation of the rod arm in the accelerometer, namely an Xm axis, a Ym axis and a Zm axis in an m system; omega _xc、ω_yc and omega _zc are components of the angular rate in the m-system of the Xm-axis, the Ym-axis and the Zm-axis;

S604, bringing a _xb、a_yb、a_zb and omega _xc、ω_yc、ω_zc in the step S603 into an inertial navigation solution equation, and obtaining a navigation result of the biaxial rotation inertial navigation through solution, namely, a navigation result after real-time compensation of dynamic errors of the biaxial rotation inertial navigation.