CN115265590A

CN115265590A - Double-shaft rotation inertial navigation dynamic error suppression method

Info

Publication number: CN115265590A
Application number: CN202210835839.1A
Authority: CN
Inventors: 涂勇强; 蔡庆中; 杨功流; 李晶; 尹洪亮
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2022-07-15
Filing date: 2022-07-15
Publication date: 2022-11-01
Anticipated expiration: 2042-07-15
Also published as: CN115265590B

Abstract

The invention discloses a method for inhibiting 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 the biaxial rotation inertial navigation in a navigation coordinate system; s3, constructing a thirty-six-dimensional Kalman filter; s4, the double-shaft indexing mechanism rotates according to the designed indexing path, and angular rate data and specific force data in the process are used as calibration data; s5, processing the 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 arm in the accelerometer by using the calibration parameters, and further resolving to obtain a navigation result; the method comprehensively considers zero offset, scale factors, installation errors, accelerometer second-order nonlinear coefficients and biaxial rotation inertial navigation dynamic errors caused by an inner rod arm of the accelerometer, and is simple and convenient to apply, high in precision and good in practicability.

Description

Double-shaft rotation inertial navigation dynamic error suppression method

Technical Field

The invention relates to the technical field of double-shaft rotation inertial navigation error calibration and suppression, in particular to a method for suppressing a dynamic error of double-shaft rotation inertial navigation.

Background

The biaxial rotation inertial navigation consists of an Inertial Measurement Unit (IMU) and an indexing mechanism, and the working principle is as follows: the IMU is installed on the indexing mechanism, so that the IMU can rotate relative to a fixed coordinate system shaft in the navigation process, and the IMU modulates constant errors of the inertial device into periodic variation with a mean value of zero through specific rotation, so that the navigation precision of the double-shaft rotation inertial navigation during long navigation can be greatly improved on the precision level of the existing inertial device. Therefore, the biaxial rotational inertial navigation system is widely applied to applications requiring a high-precision inertial navigation system, such as: in carriers for ships, combat vehicles, airplanes, etc.

In the practical use of the biaxial rotation inertial navigation, although a reasonable biaxial transposition scheme can completely modulate the constant zero offset of an inertial device in an IMU, the reasonable biaxial transposition scheme cannot modulate the scale factor error, the installation error, the accelerometer second-order nonlinear coefficient and the dynamic error caused by an arm in an accelerometer, wherein the inertial device is excited by the movement of a carrier. Therefore, in order to improve the precision of the biaxial rotational inertial navigation in a dynamic environment, the scale factor error, the installation error, the second-order nonlinear coefficient of the accelerometer and the arm in the accelerometer of the inertial device of the biaxial rotational inertial navigation need to be accurately calibrated, and compensation is performed after calibration so as to inhibit the dynamic error of the biaxial rotational inertial navigation.

In order to achieve the purpose, the published invention patent CN103575296B provides a self-calibration method of a dual-axis rotational inertial navigation system, which optimizes a calibration test path by using a genetic algorithm and calibrates zero offset, scale factors and installation errors of inertial devices in a dual-axis rotational inertial navigation IMU by processing calibration data by using a least square method; the published patent CN104165638B of the invention provides a multi-position autonomous calibration method of a double-shaft rotation inertial navigation system, the method utilizes Kalman filtering and least square method to calibrate zero offset, scale factor and installation error of a gyroscope and an accelerometer; the published invention patent CN108981751A discloses an eight-position online calibration method of a dual-axis rotary inertial navigation system, which calibrates the zero offset, the scale factor and the installation error of an IMU. The existing method can better mark the zero offset, the scale factor and the installation error of the IMU; however, in the above solutions, the accelerometer second-order nonlinear coefficient and the biaxial rotational inertial navigation dynamic error caused by the arm in the accelerometer are not considered, so that the problem that the biaxial rotational inertial navigation still has a large error in a dynamic environment is caused.

Therefore, in order to overcome the problem that the error of the biaxial rotational inertial navigation in a dynamic environment is large due to the fact that the second-order nonlinear coefficient of the accelerometer and the dynamic error of the biaxial rotational inertial navigation caused by the inner lever arm of the accelerometer are not considered in the conventional method, a simple, convenient and high-precision biaxial rotational inertial navigation dynamic error suppression method which comprehensively considers the zero offset, the scale factor, the installation error, the second-order nonlinear coefficient of the accelerometer and the inner lever arm of the accelerometer needs to be provided.

Disclosure of Invention

The invention aims to provide a biaxial rotational inertial navigation dynamic error suppression method for solving the problem that the biaxial rotational inertial navigation has larger error in a dynamic environment due to the fact that the biaxial rotational inertial navigation dynamic error caused by the accelerometer second-order nonlinear coefficient and the accelerometer inner rod arm is not considered in the conventional biaxial rotational inertial navigation error calibration and suppression method.

Therefore, 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 shaft system, an accelerometer sensitive shaft system, an IMU coordinate system, a geocentric inertial coordinate system, a terrestrial coordinate system and a navigation coordinate system, and determining an installation error matrix of a gyro and an installation error matrix of an accelerometer;

s2, determining an error equation of the biaxial rotation inertial navigation system in a navigation coordinate system based on zero offset, scale factors, installation errors, accelerometer second-order nonlinear coefficients and errors caused by an inner lever arm of an 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 Kalman filtering estimationA feedback compensated version of the result; wherein, the state quantity of the thirty-six-dimensional Kalman filter comprises an attitude error angle of the biaxial rotation inertial navigation

Speed error delta V, position error delta P, and calibration parameter error X of gyroscope_gError X of calibration parameter of accelerometer_aSecond order non-linear coefficient calibration error X of accelerometer_Ka2Error of inner rod arm X_r；

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

s5, processing the calibration data in 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 from an initial value along with the multiple transposition of the step S4, 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 an initial alignment result of biaxial rotation and instrument parameters; in the state quantity estimated value in the optimal Kalman filter, the state quantity component related to the error of the inertial device is a calibration parameter;

and S6, substituting the calibration parameters into a calibration model of the gyroscope and a calibration model of the accelerometer to obtain an angular rate and a specific force which are output after calibration, obtaining an acceleration compensated by an arm in the accelerometer based on the angular rate and the specific force after calibration, and further calculating to obtain a navigation result of the biaxial rotational inertial navigation after dynamic error real-time compensation.

Further, the specific implementation steps of step S1 are:

s101, constructing a gyro sensitive axis system, namely a g system, wherein the coordinate system takes the measuring central points of three gyros as a coordinate origin, an Xg axis is consistent with the sensitive axis direction of the X-direction gyro, a Yg axis is consistent with the sensitive axis direction of the Y-direction gyro, and a Zg axis is consistent with the sensitive axis direction of the Z-direction gyro;

s102, constructing an accelerometer sensitive axis system, namely an a system, wherein the coordinate system takes the coordinate origin of the g system as the coordinate origin, the direction of an Xa axis is consistent with that of the sensitive axis of the X-direction accelerometer, the direction of a Ya axis is consistent with that of the sensitive axis of the Y-direction accelerometer, and the direction of a Za axis is consistent with that of the sensitive axis of the Z-direction accelerometer;

s103, constructing an IMU coordinate system, namely an m system, wherein the coordinate system takes the coordinate origin of the g system as the coordinate origin, the Xm axis is consistent with the Xg axis of the gyro sensitive axis, the 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_yzThe Zm axis is a gyro sensitive axis Zg axis which rotates by a small angle gamma around the Xm axis_zxAnd then rotated by a small angle gamma about the Ym axis_zy；

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 in the equatorial plane of the earth, the Xi axis points to the spring equinox, and the Zi axis is the earth rotation axis and points to the north pole;

s105, constructing an earth coordinate system, namely an e system, wherein the earth center is taken as a coordinate origin, xe and Ye axes are in the earth equatorial plane, xe points to the prime meridian, and 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 geographical coordinate system, the origin of coordinates of the n system is the origin of coordinates of an IMU coordinate system, an Xn axis points to the east, a Yn axis points to the north, and a Zn axis points to the sky;

s107, based on the gyro sensitive axis system and the IMU coordinate system, the installation error matrix of the gyro has the expression:

in the formula (I), the compound is shown in the specification,

is a mounting error matrix of the gyro, gamma_yz、γ_zyAnd gamma_zxFor three mounting error angles of the gyro-sensitive axis system relative to the IMU coordinate system, in particular, gamma_yzIndicating the angle of deflection, gamma, of the Y-axis gyro axis of sensitivity Yg about the Zm axis of the m-system_zyIndicating the angle of deflection, gamma, of the Z-axis of the gyro's sensitive axis Zg about the Ym-axis of the m-system_zxThe deflection angle of a Z-direction gyro sensitive axis Zg around an Xm axis of an m system is represented;

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

in the formula (I), the compound is shown in the specification,

is a mounting error matrix of the accelerometer, alpha_xz、α_xy、α_yz、α_yx、α_zyAnd alpha_zxFor six mounting error angles of the accelerometer sensitive axis system relative to the IMU coordinate system, in particular, alpha_xzRepresenting the deflection angle, alpha, of the sensitive axis Xa of the X-direction accelerometer about the Zm axis of the m-system_xyRepresenting the angle of deflection, alpha, of the sensitive axis Xa of the X-direction accelerometer about the Ym axis of the system m_yzThe deflection angle alpha of the sensitive axis Ya of the Y-direction accelerometer around the Zm axis of the m system_yxRepresenting the deflection angle, alpha, of the sensitive axis Ya of the Y-direction accelerometer around the Xm axis of the m system_zyRepresenting the deflection angle, alpha, of the axis Za of the sensitive axis of the Z-direction accelerometer about the Ym axis of the m-system_zxThe deflection angle of the sensing axis Za of the Z-direction accelerometer around the Xm axis of the m system is shown.

Further, the specific implementation steps of step S2 are:

an error equation of the biaxial rotational inertial navigation in a navigation coordinate system (n system) is expressed as follows:

in the formula (I), the compound is shown in the specification,

is composed of

The derivative with respect to time is,

is the attitude error angle of the biaxial rotational inertial navigation,

and

an east error angle, a north error angle and a sky error angle of the biaxial rotational inertial navigation are respectively;

is the rotation angular rate of n relative to i, which is generated by the rotation of earth and the movement of carrier;

in resolving for navigation

The estimation error of (2);

a coordinate transformation matrix from an m system to an n system;

is the measurement error of the gyroscope;

is delta VⁿDerivative with respect to time, δ VⁿIs the velocity error, delta V, of the biaxial rotational inertial navigationⁿ＝[δV_E δV_N δV_U]^T，δV_E、δV_NAnd δ V_UEast-direction speed error, north-direction speed error and sky-direction speed error respectively; f. ofⁿIs a specific force under n;

is the earth rotation angular rate;

angular velocity generated for motion of the carrier about the earth; (ii) a VⁿIs the velocity, V, of a biaxial rotational inertial navigationⁿ＝[V_E V_N V_U]^T，V_E、V_NAnd V_UEast speed, north speed and sky speed of the biaxial rotation inertial navigation system respectively;

is composed of

The error of (2);

is composed of

An error of (2); δ f^mIs the measurement error of the accelerometer;

is the accelerometer inner arm error; δ g is the gravity vector error;

is the derivative of δ L with respect to time, δ L being the latitude error;

is the derivative of δ λ with respect to time, δ λ is the longitude error;

is the derivative of δ h with respect to time, δ h being the height error; l, λ and h are local geographical latitude, longitude and altitude, respectively; r_MAnd R_NThe radiuses of the local earth meridian circle and the prime unit circle are respectively;

wherein the measurement error of the gyroscope

The expression of (a) is:

in the formula (I), the compound is shown in the specification,

measured values of the gyroscope under the system m; delta K_GAn error matrix that is the scale factor of the gyroscope and the mounting error,

and

respectively scale factor of X-direction gyro

Y-direction gyro scale factor

And Z-direction gyro scale factorNumber of

The error of (2); delta gamma_yz、δγ_zyAnd δ γ_zxAre respectively gyro installation error angle gamma_yz、γ_zyAnd gamma_zxAn error of (2); epsilon^mThe zero offset error of the gyroscope is expressed as: epsilon^m＝[ε_x ε_y ε_z]^TIn the formula, epsilon_x、ε_yAnd epsilon_zZero offset errors of the X-direction gyroscope, the Y-direction gyroscope and the Z-direction gyroscope respectively;

measurement error δ f of accelerometer^mThe expression of (c) is:

in the formula (I), the compound is shown in the specification,

measured values of the accelerometer under the m series; delta K_AIs the error matrix of the scale factor and mounting error of the accelerometer,

and

scale factors for the respective X-direction accelerometer

Scale factor of Y-direction accelerometer

And Z-direction accelerometer scale factor

The error of (2); delta alpha_xz、δα_xy、δα_yz、δα_yx、δα_zyAnd delta alpha_zxRespectively an accelerometer mounting error angle alpha_xz、α_xy、α_yz、α_yx、α_zyAnd alpha_zxAn error of (2); delta K_A2Is a calibration error matrix of second order nonlinear coefficients of the accelerometer,

δK_ax2、δK_ay2and δ K_az2Respectively, the second-order nonlinear coefficient K of the X-direction accelerometer_ax2Calibration error, second-order nonlinear coefficient K of Y-direction accelerometer_ay2Calibration error of the accelerometer and second-order nonlinear coefficient K of the accelerometer in Z direction_az2The calibration error of (2);

for 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 are respectively;

accelerometer inner lever arm error

The expression of (c) is:

in the formula (I), the compound is shown in the specification,

and

respectively error of inner rod arm

In m is X_mAxis, Y_mAxis and Z_mThe component on the axis of the light beam,

wherein the content of the first and second substances,

and

respectively measured values of the gyroscope in the m system

At X_mAxis, Y_mAxis and Z_mAn on-axis component; delta r_x、δr_yAnd δ r_zRespectively an X-direction accelerometer inner lever arm r_xInner lever arm r of Y-direction accelerometer_yAnd Z-direction accelerometer inner lever arm r_zThe error of (2).

Further, the step S3 is implemented as follows:

s301, constructing state quantity X of thirty-six-dimensional Kalman filter³⁶：

In the formula,

is the attitude error angle of the biaxial rotational inertial navigation,

δ V is the speed error, δ V = [ δ V ]_E δV_N δV_U]^T(ii) a δ P is the position error, δ P = [ δ L δ h]^T；X_gIs the error of the calibration parameter of the gyroscope,

X_afor the error in the calibration parameters of the accelerometer,

X_Ka2error calibration for second-order non-linear coefficients of accelerometers, X_Ka2＝[δK_ax2 δK_ay2 δK_az2]^T；X_rFor errors in the arms of the inner rod, X_r＝[δr_x δr_y δr_z]^T；

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

in the formula (I), the compound is shown in the specification,

at F³³In (1),

F³⁶in (1),

G³⁶to measure the noise the input matrix is,

u is the noise of the measurement and is,

wherein u is_gAs measurement noise of the gyro, u_aMeasurement noise for an accelerometer;

s303, constructing an observation equation of the thirty-six-dimensional Kalman filter: z = H³⁶X³⁶+v，

Wherein Z is an observed quantity, and when the biaxial rotational inertial navigation is kept in a stationary state by taking the velocity as the observed quantity and during calibration, Z = [ V ]_E V_N V_U]^T；H³⁶To observe the matrix, H³⁶＝[0_3×3 I₃ 0_3×30]，I₃In an identity matrix of three rows and three columns, i.e.

0_3×30Is a zero matrix of three rows and thirty columns, 0_3×3A zero matrix with three rows and three columns; v is the observed noise;

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

in the formula (I), the compound is shown in the specification,

is composed of

The anti-symmetric matrix of (a) is,

for biaxial rotary inertial navigation

Calculating the result of (1);

v for biaxial rotational inertial navigationⁿCalculating the result of (1);

the calculation result is the L of the biaxial rotation inertial navigation;

calculating a lambda calculation result of the biaxial rotation inertial navigation;

the calculation result is the h of the biaxial rotation inertial navigation; ,

k before feedback compensation for Kalman filtering estimation result_G；

ε before compensation for Kalman filter estimation result feedback^m；，

K before feedback compensation for Kalman filtering estimation result_A；

Before feedback compensation for Kalman filtering estimation result

K before feedback compensation for Kalman filtering estimation result_A2；

R before feedback compensation for Kalman filtering estimation results_x；

R before feedback compensation for Kalman filter estimation results_y；

R before feedback compensation for Kalman filter estimation results_z。

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

initial positions are corresponded based on the order 0: standing for 10 minutes in a posture that the Xm axis of the biaxial rotation inertial navigation system faces east, the Ym axis of the biaxial rotation inertial navigation system faces north and the Zm axis of the biaxial rotation inertial navigation system faces sky;

sequence 1: the middle frame shaft is taken as a rotating shaft and rotates 90 degrees clockwise; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face east, sky, and south, respectively; after the transposition is finished, standing for 180s;

sequence 2: clockwise rotating 180 degrees by taking the middle frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face east, ground, and north, respectively; after the transposition is finished, standing for 180s;

sequence 3: clockwise rotating 180 degrees by taking the middle frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face east, sky, and south, respectively; after the transposition is finished, standing for 180s;

sequence 4: rotating the inner frame shaft by 90 degrees clockwise by using the inner frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation face the sky, the Ym axis, and the Zm axis, respectively; after transposition is completed, standing for 180s;

sequence 5: clockwise rotating 180 degrees by taking the inner frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotary inertial navigation system face the ground, the Ym axis, and the Zm axis, respectively; after the transposition is finished, standing for 180s;

sequence 6: rotating 180 degrees clockwise with the inner frame shaft as the rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face the sky, the west, and the south, respectively; after the transposition is finished, standing for 180s;

sequence 7: the middle frame shaft is taken as a rotating shaft and rotates 90 degrees clockwise; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotary inertial navigation system face south, west, and ground; after the transposition is finished, standing for 180s;

sequence 8: clockwise rotating 180 degrees by taking the middle frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face north, west, and sky, respectively; after transposition is completed, standing for 180s;

sequence 9: clockwise rotating 180 degrees by taking the middle frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotary inertial navigation system face south, west, and ground; after the transposition is finished, standing for 180s;

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

sequence 11: clockwise rotating by 90 degrees by taking the middle frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face north, west, and sky, respectively; after the transposition is finished, standing for 180s;

sequence 12: the middle frame shaft is taken as a rotating shaft and rotates 90 degrees clockwise; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation face the sky, the Ym axis, and the Zm axis, respectively; after transposition is completed, standing for 180s;

sequence 13: rotating the inner frame shaft by 90 degrees clockwise by using the inner frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation face the west, the Ym axis, and the Zm axis, respectively; after transposition is completed, standing for 180s;

sequence 14: clockwise rotates 90 degrees by taking the inner frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotary inertial navigation system face the ground, the Ym axis, and the Zm axis, respectively; after the transposition is finished, standing for 180s;

sequence 15: rotating the inner frame shaft by 90 degrees clockwise by using the inner frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face east, sky, and south, respectively; after the transposition is finished, standing for 180s;

sequence 16: the middle frame shaft is taken as a rotating shaft and rotates 90 degrees clockwise; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face east, south, and ground, respectively; after the transposition is finished, standing for 180s;

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

sequence 18: clockwise rotating by 90 degrees by taking the middle frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face east, north, and sky, respectively; after indexing is completed, rest is carried out for 180s.

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

Further, the specific implementation steps of step S5 are:

s501, carrying out initial value on thirty-six-dimensional state quantityAnd (4) assignment:

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; assigning the initial value of the delta P by a difference value obtained by subtracting the actual experimental position from the initial position output after the biaxial rotation inertial navigation in the step S4 is completed; x_g、X_a、X_Ka2And X_rThe initial value of (A) is assigned according to the actual conditions of the gyroscope and the accelerometer in the biaxial rotational inertial navigation;

s502, based on the initial value of the thirty-six-dimensional state quantity determined in the step S501 as the initial value of the state quantity of Kalman filtering, respectively substituting the thirty-six-dimensional state quantity constructed in the step S301 into the state equation of the thirty-six-dimensional Kalman filter constructed in the step S302 and the observation equation of the thirty-six-dimensional Kalman filter constructed in the step S303, processing calibration data by adopting a Kalman filtering algorithm and the Kalman filter constructed in the step S3, and continuously iterating and performing feedback compensation on the state quantity in the Kalman filter from the initial value 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 estimated value is an accurate calibration parameter, and the method comprises the following steps: x-direction gyro scale factor

Y-direction gyro scale factor

And Z-direction gyro scale factor

Error angle gamma for installing gyroscope_yz、γ_zyAnd gamma_zx(ii) a Zero bias of X-direction gyroscope

Zero bias of Y-direction gyroscope

And in the Z directionZero offset of gyroscope

Scale factor of X-direction accelerometer

Scale factor of Y-direction accelerometer

And Z-direction accelerometer scale factor

The error of (2); accelerometer mounting error angle alpha_xz、α_xy、α_yz、α_yx、α_zyAnd alpha_zx(ii) a Second-order nonlinear coefficient K of X-direction accelerometer_ax2Second-order nonlinear coefficient K of Y-direction accelerometer_ay2And the second-order nonlinear coefficient K of the Z-direction accelerometer_az2(ii) a Zero offset of X-direction accelerometer

Zero offset of Y-direction accelerometer

And zero offset of Z-direction accelerometer

Inner lever arm r of X-direction accelerometer_xY-direction adder inner lever arm r_yAnd an inner lever arm r of the Z-direction accelerometer_z；

Further, the specific implementation steps of step S6 are:

s601, adopting the existing sixty-four sequence rotation modulation scheme as the rotation scheme of the indexing mechanism in the biaxial rotation inertial navigation process, stopping for 10S after each rotation to a position, and obtaining the output result of the inertia device after rotation modulation, including the angular rate output by the gyroscope

And accelerateSpecific force output by the meter

S602, respectively substituting the calibration parameters obtained in the step S5 into a gyro calibration model and an accelerometer calibration model to obtain output after gyro calibration and output after accelerometer calibration; wherein, the first and the second end of the pipe are connected with each other,

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

in the formula (I), the compound is shown in the specification,

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

in the formula (I), the compound is shown in the specification,

s603, by utilizing the output after the gyro calibration and the output after the accelerometer calibration obtained in the step S602, utilizing an inner lever arm r of the X-direction accelerometer_xInner lever arm r of Y-direction accelerometer_yAnd an inner lever arm r of the Z-direction accelerometer_zThe acceleration data is compensated in real time, and the specific formula is as follows:

in the formula, a_xb、a_ybAnd a_zbComponents of an Xm axis, a Ym axis and a Zm axis in an m system of the real-time result of the acceleration compensated by the inner rod arm of the accelerometer; a is a_xc、a_ycAnd a_zcThe components of an Xm axis, a Ym axis and a Zm axis in an m system of an acceleration real-time result before compensation of an arm in the accelerometer are obtained; omega_xc、ω_ycAnd omega_zcIs the component of the angular velocity in the m system on the Xm axis, ym axis and Zm axis;

s604, converting a in the step S603_xb、a_yb、a_zbAnd ω_xc、ω_yc、ω_zcAnd (4) bringing an inertial navigation resolving equation into the inertial navigation to obtain a navigation result of the double-shaft rotational inertial navigation, namely the navigation result obtained by compensating the dynamic error of the double-shaft rotational inertial navigation in real time by adopting the method.

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

(1) The method for restraining the dynamic error of the biaxial rotational inertial navigation is simple and convenient and high in precision, and the zero offset, the scale factor, the installation error, the second-order nonlinear coefficient of the accelerometer and the dynamic error of the biaxial rotational inertial navigation caused by the inner rod arm of the accelerometer of the IMU are comprehensively considered;

(2) After the method is adopted for calibration compensation, the speed error caused by the dynamic state is obviously reduced, the effect can reach 90%, the positioning precision of the biaxial rotation inertial navigation under the dynamic environment can be improved by about 8 meters, the correctness and the accuracy of the method are proved, the dynamic error of the biaxial rotation inertial navigation can be well inhibited, and the practicability is good.

Drawings

FIG. 1 is a schematic flow chart of a biaxial rotational inertial navigation dynamic error suppression method according to the present invention;

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

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

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

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

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

Detailed Description

The invention will be further described with reference to the following figures and specific examples, which are not intended to limit the invention in any way.

As shown in fig. 1, the method for suppressing dynamic error of biaxial rotational inertial navigation includes the following steps:

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

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

(1) The gyro-sensitive axis system, also referred to as the g-system for short, is expressed as: o-XgYgZg; the coordinate system takes the measuring central points of three gyroscopes as coordinate origin points (o points), the Xg axis of the coordinate system is consistent with the sensitive axis direction of the X-direction gyroscope, the Yg axis of the coordinate system is consistent with the sensitive axis direction of the Y-direction gyroscope, and the Zg axis of the coordinate system is consistent with the sensitive axis direction of the Z-direction gyroscope; in the IMU of the biaxial rotation inertial navigation, three gyroscopes cannot be guaranteed to be installed in a strict orthogonal mode, so that a system g is not an orthogonal coordinate system;

(2) The accelerometer sensitive axis system, also referred to as a system for short, is expressed as: o-XaYaZa; the coordinate origin of the coordinate system is coincided 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 consistent with the sensitive axis direction of the X-direction accelerometer, the Ya axis is consistent with the sensitive axis direction of the Y-direction accelerometer, and the Za axis is consistent with the sensitive axis direction of the Z-direction accelerometer; similarly, since three accelerometers cannot be installed strictly orthogonally in the IMU of the biaxial rotational inertial navigation system, the a system is not an orthogonal coordinate system;

(3) The IMU coordinate system, also referred to as m-system for short, is expressed as: o-XmYmZm; because the inertial navigation solution requires that the output of each inertial device is projected into the same orthogonal coordinate system, the coordinate system is an orthogonal coordinate system used for projecting the output of the gyroscope and the accelerometer into an orthogonal vector; as shown in fig. 2, the coordinate origin of the coordinate system coincides with the coordinate origin of the g system, that is, the Xm axis coincides with the Xg axis of the gyro-sensitive axis, and the Ym axis is in the plane formed by the Xg axis and the Yg axis and is different from the Yg axis by a small angle γ with the coordinate origin of the g system (point o) as the coordinate origin_yzThe Zm axis is a gyro sensitive axis Zg axis which rotates around the Xm axis by a small angle gamma_zxRotated by a small angle gamma about the Ym axis_zy；

(4) The centroid inertial frame, also called the i-frame for short, is denoted as o_e-XiYiZi, the coordinate system being a reference for the output of the inertial device, its origin of coordinates o_eThe Xi axis and the Yi axis are in the equatorial plane of the earth, and the Xi axis points to the vernal equinox (namely one of intersection points of the intersection line of the equatorial plane and the ecliptic plane and the celestial sphere), and the Zi axis is the rotation axis of the earth and points to the north pole;

(5) Terrestrial coordinate system, also abbreviated as e-system, denoted o_e-XeYeZe; origin of coordinates o of the coordinate system_eThe axis Xe and Ye are in the equatorial plane of the earth, with Xe pointing to the meridian of origin and the axis Ze being the axis of rotation of the earth and pointing to the North Pole; the earth coordinate system is fixedly connected with the earth, and the angular rate of the e system relative to the i system is the rotational angular rate of the earth;

(6) A navigational coordinate system, also referred to as the n system for short, denoted o-xnylzn; the coordinate system is used as a coordinate system adopted by inertial navigation when navigation parameters are solved, specifically a northeast geographic coordinate system, wherein the origin o of the coordinate system is the origin of the 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 relationship of the n system relative to the e system is the geographic position of the carrier;

based on the gyro sensitive axis system (g system) and the IMU coordinate system (m system) which are constructed, the expression of the installation error matrix of the gyro can be determined as follows:

in the formula (I), the compound is shown in the specification,

is a mounting error matrix of the gyro, gamma_yz、γ_zyAnd gamma_zxFor three mounting error angles of the gyro-sensitive axis system relative to the IMU coordinate system, in particular, gamma_yzIndicating the angle of deflection, gamma, of the Y-axis gyro sensitive axis Yg about the Zm-axis of the m-system_zyIndicating the angle of deflection, gamma, of the Z-axis of gyro sensitivity Zg about the Ym-axis of the m-system_zxThe deflection angle of a Z-direction gyro sensitive axis Zg around an Xm axis of an m system is represented;

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

in the formula (I), the compound is shown in the specification,

is the mounting error matrix of the accelerometer, alpha_xz、α_xy、α_yz、α_yx、α_zyAnd alpha_zxFor six mounting error angles, in particular alpha, of the accelerometer sensitive axis system relative to the IMU coordinate system_xzRepresenting the angle of deflection, alpha, of the sensitive axis Xa of the X-direction accelerometer about the Zm axis of the m-system_xyRepresenting the angle of deflection, alpha, of the sensitive axis Xa of the X-direction accelerometer about the Ym axis of the system m_yzThe deflection angle alpha of the sensitive axis Ya of the Y-direction accelerometer around the Zm axis of the m system_yxRepresenting the deflection angle, alpha, of the sensitive axis Ya of the Y-direction accelerometer around the Xm axis of the m system_zyRepresenting the deflection angle, alpha, of the axis Za of the sensitive axis of the Z-direction accelerometer about the Ym axis of the m-system_zxRepresenting sense axis Za of a Z-direction accelerometer about m-systemThe deflection angle of the Xm axis;

s2, determining an error equation of the biaxial rotational inertial navigation under a navigation coordinate system (n system) based on zero offset, scale factors, installation errors, second-order nonlinear coefficients of the accelerometer and errors caused by lever arms in the accelerometer, wherein the expression is as follows:

in the formula (I), the compound is shown in the specification,

is composed of

The derivative with respect to time is determined,

is the attitude error angle of the biaxial rotational inertial navigation,

and

east error angle of biaxial rotation inertial navigationA north error angle and a sky error angle;

in resolving for navigation

The estimated error of (2);

a coordinate transformation matrix from m system to n system;

is the measurement error of the gyroscope;

is delta VⁿDerivative with respect to time, δ VⁿIs the velocity error, delta V, of biaxial rotational inertial navigationⁿ＝[δV_E δV_N δV_U]^T，δV_E、δV_NAnd δ V_UEast-direction speed error, north-direction speed error and sky-direction speed error respectively; f. ofⁿIs a specific force under n;

is the earth rotation angular rate;

angular velocity generated for motion of the carrier about the earth; (ii) a VⁿIs the velocity, V, of a biaxial rotational inertial navigationⁿ＝[V_E V_N V_U]^T，V_E、V_NAnd V_UEast-direction speed, north-direction speed and sky-direction speed of the biaxial rotational inertial navigation system are respectively;

is composed of

An error of (2);

is composed of

The error of (2); δ f^mIs the measurement error of the accelerometer;

is the arm error in the accelerometer; δ g is the gravity vector error;

is the derivative of δ L with respect to time, δ L being the latitude error;

is the derivative of δ λ with respect to time, δ λ is the longitude error;

wherein the measurement error of the gyroscope

The expression of (c) is:

in the formula (I), the compound is shown in the specification,

and

respectively scale factor of X-direction gyro

Y-direction gyro scale factor

And Z-direction gyro scale factor

The error of (2); delta gamma_yz、δγ_zyAnd δ γ_zxAre respectively gyro installation error angle gamma_yz、γ_zyAnd gamma_zxAn error of (2);

ε^mthe zero offset error of the gyroscope is expressed as follows: epsilon^m＝[ε_x ε_y ε_z]^T，

In the formula, epsilon_x、ε_yAnd ε_zZero offset errors of the X-direction gyroscope, the Y-direction gyroscope and the Z-direction gyroscope respectively;

measurement error δ f of accelerometer^mThe expression of (c) is:

in the formula (I), the compound is shown in the specification,

and

scale factors for the respective X-direction accelerometer

Scale factor of Y-direction accelerometer

And a Z-direction accelerometer scaling factor

The error of (2); delta alpha_xz、δα_xy、δα_yz、δα_yx、δα_zyAnd delta alpha_zxRespectively, an accelerometer mounting error angle alpha_xz、α_xy、α_yz、α_yx、α_zyAnd alpha_zxAn error of (2); delta K_A2Is a calibration error matrix of second order nonlinear coefficients of the accelerometer,

δK_ax2、δK_ay2and δ K_az2Second order nonlinear coefficients K of the X-direction accelerometer respectively_ax2Calibration error, second-order nonlinear coefficient K of Y-direction accelerometer_ay2Calibration error of the accelerometer and second-order nonlinear coefficient K of the accelerometer in Z direction_az2The calibration error of (2);

is 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 (c) is:

in the formula (I), the compound is shown in the specification,

and

respectively error of inner rod arm

In the m system X_mAxis, Y_mAxis and Z_mThe component on the axis of the light beam,

wherein the content of the first and second substances,

and

respectively measured values of the gyroscope in the m system

At X_mAxis, Y_mAxis and Z_mA component on the axis; delta r_x、δr_yAnd δ r_zRespectively an inner lever arm r of an X-direction accelerometer_xInner lever arm r of Y-direction accelerometer_yAnd Z-direction accelerometer inner lever arm r_zThe error of (2);

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 specific implementation steps are as follows:

s301, constructing state quantity X of thirty-six-dimensional Kalman filter³⁶Comprises the following steps:

in the formula (I), the compound is shown in the specification,

is the attitude error angle of the biaxial rotational inertial navigation,

δ V is the speed error, δ V = [ δ V ]_E δV_N δV_U]^T(ii) a δ P is a position error, δ P = [ δ L δ h]^T；X_gIs the error of the calibration parameter of the gyroscope,

X_afor the error in the calibration parameters of the accelerometer,

X_Ka2error calibration for second order nonlinear coefficients of accelerometers, X_Ka2＝[δK_ax2 δK_ay2 δK_az2]^T；X_rError of the inner lever arm, X_r＝[δr_x δr_y δr_z]^T；

in the formula (I), the compound is shown in the specification,

wherein, in F³³Each non-zero matrix element is:

F³⁶in the step (1), the first step,

G³⁶to measure the noise the input matrix is,

u is the noise of the measurement and is,

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

Z＝H³⁶X³⁶+v，

0_3×30Zero matrix of three rows and thirty columns, 0_3×3A zero matrix with three rows and three columns; v is the observation noise;

in the formula (I), the compound is shown in the specification,

is composed of

Of antisymmetric matrices, i.e.

For biaxial rotational inertial navigation

Calculating the result of (1);

v for biaxial rotary inertial navigationⁿCalculating the result of (2);

calculating the result of the L of the biaxial rotation inertial navigation;

calculating the lambda of the biaxial rotation inertial navigation;

calculating the result of h of biaxial rotation inertial navigation; ,

k before feedback compensation for Kalman filtering estimation result_G；

ε before compensation for Kalman filter estimation result feedback^m；，

K before feedback compensation for Kalman filtering estimation result_A；

Before feedback compensation for Kalman filtering estimation results

K before feedback compensation for Kalman filtering estimation result_A2；

R before feedback compensation for Kalman filtering estimation results_x；

R before feedback compensation for Kalman filter estimation results_y；

R before feedback compensation for Kalman filter estimation results_z；

S4, designing a transposition path of the double-shaft transposition mechanism in the calibration test and carrying out the calibration test;

the specific steps of step S4 are:

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 perpendicular to each other and are in the same plane; the indexing path of the double-shaft indexing mechanism is controlled by controlling the rotation of the middle frame shaft and the inner frame shaft, so that the IMU coordinate system continuously changes the posture; setting the rotating speed of the double-shaft indexing mechanism to be 5 degrees/s; the indexing path is shown in table 1 below, specifically:

sequence 0: the double-shaft indexing mechanism is at an initial position, wherein the frame shaft faces east, the inner frame shaft faces sky, correspondingly, the Xm shaft faces east, the Ym shaft faces north and the Zm shaft faces sky of the double-shaft rotary inertial navigation system; the dual-axis indexing mechanism is initially static for 10 minutes, so that dual-axis rotary inertial navigation is initially aligned in the static process, initial navigation resolving results including attitude angles and speeds are obtained, and then the dual-axis rotary inertial navigation enters a navigation resolving state;

sequence 1: the middle frame shaft is taken as a rotating shaft, the clockwise rotation is carried out for 90 degrees, the posture of the rotating indexing mechanism is recorded as a sequence 1, and the specific posture corresponding to the biaxial rotation inertial navigation is as follows: xm axis towards east, ym axis towards sky, zm axis towards south; and rest for 180s at the rotated order 1 position;

sequence 2: the middle frame shaft is taken as a rotating shaft, the clockwise rotation is 180 degrees, the posture of the rotating indexing mechanism is recorded as a sequence 2, and the specific posture corresponding to the biaxial rotation inertial navigation is as follows: xm-axis towards east, ym-axis towards ground, zm-axis towards north; and stationary for 180s at the rotated order 2 position;

sequence 3: the middle frame shaft is taken as a rotating shaft, the clockwise rotation is 180 degrees, the posture of the rotating indexing mechanism is recorded as a sequence 3, and the specific posture corresponding to the biaxial rotation inertial navigation is as follows: xm axis towards east, ym axis towards sky, zm axis towards south; and stationary for 180s at the rotated sequence 3 position;

sequence 4: the inner frame shaft is used as a rotating shaft, the clockwise rotation is carried out for 90 degrees, the posture of the rotating indexing mechanism is recorded as a sequence 4, and the specific posture corresponding to the biaxial rotation inertial navigation is as follows: xm axis towards the sky, ym axis towards the west, and Zm axis towards the south; and rest for 180s at the rotated order 4 position;

sequence 5: the inner frame shaft is used as a rotating shaft, the clockwise rotation is 180 degrees, the posture of the rotating indexing mechanism is recorded as a sequence 5, and the specific posture corresponding to the biaxial rotation inertial navigation is as follows: xm axis towards the ground, ym axis towards the east, zm axis towards the south; and rest for 180s at the rotated position of order 5;

sequence 6: the inner frame shaft is used as a rotating shaft, the rotating shaft rotates 180 degrees clockwise, the rotating attitude of the indexing mechanism is recorded as an order 6, and the corresponding specific attitude of the biaxial rotation inertial navigation is as follows: xm axis towards the sky, ym axis towards the west, and Zm axis towards the south; and rest for 180s at the rotated position of order 6;

sequence 7: taking the middle frame shaft as a rotating shaft, rotating clockwise by 90 degrees, recording the attitude of the rotating indexing mechanism as an order of 7, and taking the specific attitude corresponding to the biaxial rotation inertial navigation as follows: xm-axis towards south, ym-axis towards west, zm-axis towards ground; and rest for 180s at the rotated position of order 7;

sequence 8: the middle frame shaft is used as a rotating shaft, the clockwise rotation is 180 degrees, the rotating indexing mechanism posture is recorded as a sequence 8, and the specific posture corresponding to the biaxial rotation inertial navigation is as follows: xm axis facing north, ym axis facing west, and Zm axis facing sky; and rest for 180s at the rotated position of order 8;

sequence 9: the middle frame shaft is taken as a rotating shaft, the clockwise rotation is 180 degrees, the rotating indexing mechanism posture is recorded as a sequence 9, and the specific posture corresponding to the biaxial rotation inertial navigation is as follows: xm-axis towards south, ym-axis towards west, zm-axis towards ground; and rest for 180s at the rotated position of order 9;

sequence 10: taking the middle frame shaft as a rotating shaft, rotating clockwise by 90 degrees, recording the posture of the rotating indexing mechanism as a sequence 10, and taking the specific posture corresponding to the biaxial rotation inertial navigation as follows: xm-axis towards ground, ym-axis towards west, zm-axis towards north; and rest for 180s at the rotated position of sequence 10;

sequence 11: the middle frame shaft is taken as a rotating shaft, the clockwise rotation is carried out for 90 degrees, the posture of the rotating indexing mechanism is recorded as a sequence 11, and the specific posture 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 rest for 180s at the rotated position of sequence 11;

sequence 12: taking the middle frame shaft as a rotating shaft, rotating clockwise by 90 degrees, recording the attitude of the rotating indexing mechanism as a sequence of 12, and taking the specific attitude corresponding to the biaxial rotation inertial navigation as follows: xm axis towards the sky, ym axis towards the west, and Zm axis towards the south; and stationary for 180s at the rotated position of sequence 12;

sequence 13: the inner frame shaft is used as a rotating shaft, the clockwise rotation is carried out for 90 degrees, the posture of the rotating indexing mechanism is recorded as a sequence 13, and the specific posture corresponding to the biaxial rotation inertial navigation is as follows: xm axis toward west, ym axis toward ground, zm axis toward south; and rest for 180s at the rotated position of sequence 13;

sequence 14: the inner frame shaft is used as a rotating shaft, the rotating shaft rotates 90 degrees clockwise, the rotating attitude of the indexing mechanism is recorded as a sequence 14, and the corresponding specific attitude of the biaxial rotation inertial navigation is as follows: xm-axis towards ground, ym-axis towards east, zm-axis towards south; and stationary for 180s at the rotated position of sequence 14;

sequence 15: the inner frame shaft is used as a rotating shaft, the rotating shaft rotates 90 degrees clockwise, the attitude of the rotating indexing mechanism is recorded as an order of 15, and the specific attitude corresponding to the biaxial rotation inertial navigation is as follows: xm axis towards east, ym axis towards sky, zm axis towards south; and rest for 180s at the rotated position of sequence 15;

sequence 16: taking the middle frame shaft as a rotating shaft, rotating clockwise by 90 degrees, recording the rotating posture of the indexing mechanism as a sequence 16, and taking the specific posture corresponding to the biaxial rotation inertial navigation as follows: xm-axis towards east, ym-axis towards south, zm-axis towards ground; and rest for 180s at the rotated position of sequence 16;

sequence 17: taking the middle frame shaft as a rotating shaft, rotating clockwise by 90 degrees, recording the rotating posture of the indexing mechanism as a sequence 17, and taking the specific posture corresponding to the biaxial rotation inertial navigation as follows: xm-axis east, ym-axis ground, zm-axis north; and rest for 180s at the rotated position of sequence 17;

sequence 18: taking the middle frame shaft as a rotating shaft, rotating clockwise by 90 degrees, recording the rotating posture of the indexing mechanism as a sequence 18, and taking the specific posture corresponding to the biaxial rotation inertial navigation as follows: xm axis towards east, ym axis towards north, zm axis towards sky; and rest for 180s at the rotated position of sequence 18;

table 1:

the whole transposition process involves 18 times of rotation sequences in total, and the rotation is stopped for 180s after each time of rotation to the specified position, namely the whole transposition path can be completed within 1 hour;

in the above-mentioned indexing path, the first nine times of rotation (sequence 1 to sequence 9) are aimed at exciting a gyro scale factor error and a mounting error, and therefore, two 180 ° rotations in one direction of each axis of the IMU are included in total; the purpose of the last nine rotations (sequence 10-sequence 18) is to excite the accelerometer scale factor and the mounting error, thus including the two positions of the finger-sky and the finger-earth for 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; because in actual calibration, the random noise of the gyroscope is large, and the estimation of the zero offset error of the gyroscope in the Kalman filter usually needs a long time, calibration path transposition is carried out twice in one calibration, so that the estimation curve of each calibration parameter error can be ensured to be completely converged, and finally, the state quantity estimation value in the Kalman filter is obtained; (ii) a

S402, starting up and preheating for at least four hours to reduce the influence of temperature change on calibration;

s403, completing a calibration experiment, namely controlling the rotation of the double-shaft indexing mechanism according to the calibration indexing path designed in the step S401, and storing angular rate data output by the gyroscope and specific force data output by the accelerometer as calibration data;

s5, processing the calibration data obtained in the step S4 by using the Kalman filter constructed in the step S3 to obtain calibration parameters, wherein the specific implementation process is as follows:

s501, initial values of thirty-six-dimensional state quantities in the thirty-six-dimensional Kalman filter are given, namely the initial values are given

An initial value of (d); wherein the content of the first and second substances,

and δ V = [ δ V ]_E δV_N δV_U]^TThe initial value is directly assigned by an initial attitude angle and an initial speed in an initial alignment result of biaxial rotation, and specifically comprises the following steps: the initial value of the attitude obtained after the indexing mechanism is static for 10 minutes in the initial state and the biaxial rotational inertial navigation is initially aligned in the step S4 is as follows:

and initial value of velocity: v₀＝[V_E0 V_N0 V_U0]^TAs

And the initial value of deltav, i.e. in the initial state,

δV＝V₀；

and the initial value of the delta P is assigned by subtracting the difference value of the actual laboratory position from the initial position output after the initial alignment is completed by the biaxial rotational inertial navigation of the step S4, and specifically comprises the following steps: 1) Obtaining laboratory position P using GPS_t＝[L_t λ_t h_t]^TWherein L is_t、λ_tAnd h_tWeft of laboratory respectivelyDegrees, longitude, and altitude; 2) The initial position output after the biaxial rotation inertial navigation of the step S4 completes the initial alignment is P₀＝[L₀ λ₀ h₀]^T(ii) a 3) The initial value of δ P is set as: [ L ]₀-L_t λ₀-λ_t h₀-h_t]^T；

X_g、X_a、X_Ka2And X_rThe initial value is assigned according to the actual conditions of the gyro and the accelerometer used by the specific biaxial rotational inertial navigation (namely, the initial value is determined after artificial consideration is carried out according to the type and the precision level of the instrument and the design characteristics of a mechanical structure);

s502, taking the initial value of the thirty-six-dimensional state quantity determined in the step S501 as the initial value of the state quantity of Kalman filtering, substituting the thirty-six-dimensional state quantity constructed in the step S301 into the state equation of the thirty-six-dimensional Kalman filter constructed in the step S302 and the observation equation of the thirty-six-dimensional Kalman filter constructed in the step S303, processing calibration data by using a Kalman filtering algorithm and the Kalman filter constructed in the step S3, enabling the state quantity in the Kalman filter to obtain continuous iteration and feedback compensation along with multiple transposition of the step S4 from the initial value, and finally obtaining the state quantity estimated value in the Kalman filter by adopting a feedback compensation mode of an estimated result determined in the step S304 for the feedback compensation;

in the state quantity estimated value, the state quantity component related to the error of the inertial device is the accurate calibration parameter obtained through the step S5, and the method includes the following steps: x-direction gyro scale factor

Y-direction gyro scale factor

And Z-direction gyro scale factor

Zero bias of Y-direction gyroscope

Zero bias with Z-direction gyro

Scale factor of X-direction accelerometer

Scale factor of Y-direction accelerometer

And Z-direction accelerometer scale factor

The error of (2); accelerometer installation error angle alpha_xz、α_xy、α_yz、α_yx、α_zyAnd alpha_zx(ii) a Second-order nonlinear coefficient K of X-direction accelerometer_ax2Second-order nonlinear coefficient K of Y-direction accelerometer_ay2And the second-order nonlinear coefficient K of the Z-direction accelerometer_az2(ii) a Zero offset of X-direction accelerometer

Zero offset of Y-direction accelerometer

And zero offset of Z-direction accelerometer

Inner lever arm r of X-direction accelerometer_xInner lever arm r of Y-direction accelerometer_yAnd Z-direction accelerometer inner lever arm r_z；

S6, substituting the calibration parameters into a calibration model to compensate the output of the double-shaft rotational inertial navigation; the specific implementation steps are as follows:

s601, adopting a common indexing mechanism rotation scheme (such as a sixty-four sequence rotation modulation scheme) as the dual-axis rotationThe rotation scheme of the indexing mechanism in the process of rotation inertial navigation and stopping for 10s after each rotation to a position are obtained, and the output result of the inertia device after rotation modulation, including the angular rate output by the gyroscope

And specific force output by the accelerometer

In step S603, the sixty-four-order rotation modulation scheme is a well-known indexing scheme for the use of dual-axis rotational inertial navigation, that is, an indexing scheme when the vehicle is mounted on a vehicle for navigation, and therefore, detailed description is not provided in this embodiment;

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

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

in the formula (I), the compound is shown in the specification,

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

in the formula (I), the compound is shown in the specification,

s603, by utilizing the output after the gyro calibration and the output after the accelerometer calibration obtained in the step S602, utilizing an inner lever arm r of the X-direction accelerometer_xInner lever arm r of Y-direction accelerometer_yAnd an inner lever arm r of the Z-direction accelerometer_zCompensating acceleration data in real timeThe body formula is:

in the formula, a_xb、a_ybAnd a_zbComponents of an Xm axis, a Ym axis and a Zm axis in an m system of the real-time result of the acceleration compensated by the inner rod arm of the accelerometer; a is_xc、a_ycAnd a_zcReal-time acceleration result f before compensation of bar arm in accelerometer^mComponents of Xm-axis, ym-axis and Zm-axis in the m-system; omega_xc、ω_ycAnd omega_zcIs angular velocity

Components of Xm-axis, ym-axis and Zm-axis in the m-system;

s604, converting the a in the step S603_xb、a_yb、a_zbAnd ω_xc、ω_ycAnd ω_zcSubstituting an inertial navigation resolving equation to obtain a navigation result of the biaxial rotation inertial navigation;

the navigation result obtained in step S604 is the navigation result obtained by performing real-time compensation on the dynamic error of the biaxial rotational inertial navigation.

In order to verify the correctness and the accuracy of the dynamic error suppression method of the biaxial rotational inertial navigation, a set of biaxial rotational inertial navigation is selected for calibration experiment, and an IMU in the selected biaxial rotational inertial navigation consists of three laser gyroscopes with zero-offset stability of 0.01 degree/h and three accelerometers with zero-offset stability of 10 mu g; the attitude control accuracy of the selected indexing mechanism of the biaxial rotary inertial navigation is 5' (1 sigma).

Firstly, use the present inventionThe method provided by the invention is used for calibrating the error parameters, X³⁶In X_g、X_a、X_Ka2And X_rThe initial value of the method is determined according to the type and the precision level of a gyroscope, an accelerometer and a mechanical structure design used by the selected biaxial rotational inertial navigation, and is as follows: x-direction gyro scale factor

Y-direction gyro scale factor

And Z-direction gyro scale factor

The initial values of (a) are all-0.84'/pulse; installation error angle gamma of gyro_yz、γ_zyAnd gamma_zxThe initial values of (A) are all 10'; zero bias of X-direction gyroscope

Zero bias of Y-direction gyroscope

Zero-offset with Z-direction gyro

The initial values of (A) are all 0.01 degree/h; scale factor of X-direction accelerometer

Scale factor of Y-direction accelerometer

And a Z-direction accelerometer scaling factor

The initial values of (a) are all 450 mu m/s/pulse; accelerometer installation error angle alpha_xz、α_xy、α_yz、α_yx、α_zyAnd alpha_zxAll initial values of (a) are 10'; second-order nonlinear coefficient K of X-direction accelerometer_ax2Second-order nonlinear coefficient K of Y-direction accelerometer_ay2And the second-order nonlinear coefficient K of the Z-direction accelerometer_az2The initial values of (a) are all 20 mu g/g2; zero offset of X-direction accelerometer

Zero offset of Y-direction accelerometer

And zero offset of Z-direction accelerometer

The initial values of (a) are all 1000 mug; inner lever arm r of X-direction accelerometer_xInner lever arm r of Y-direction accelerometer_yAnd Z-direction accelerometer inner lever arm r_zThe initial values of (A) are all 3cm;

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

table 2:

after obtaining calibration parameters, mounting the selected biaxial inertial navigation system on a test vehicle for a vehicle-mounted dynamic experiment, wherein the experiment comprises 10-minute static initial alignment and 10-minute navigation resolving, firstly, carrying out 10-minute static initial alignment under the condition that the test vehicle is in the test vehicle, entering a navigation state after the alignment is finished, starting the test vehicle to linearly start at a speed of 15m/s to simulate a dynamic environment, turning the test vehicle at 180 degrees after the biaxial rotation inertial navigation system enters the navigation state for about 4 minutes, and continuing to linearly start at a speed of 15m/s after the turning; after about 8 minutes of navigation, the test vehicle makes a 180-degree turn again, and the two rotation directions are the same.

The same set of experimental data is navigated and resolved by adopting two sets of parameters of a calibration method without considering secondary nonlinear parameters of an accelerometer and errors of a lever arm in the accelerometer and the method provided by the invention, and a navigation resolving result is compared with the speed and the position output by a GPS (global positioning system) installed on a test vehicle.

FIG. 3 (a) is a schematic diagram showing east velocity error comparison between two-axis rotational inertial navigation before and after dynamic error compensation; fig. 3 (b) is a schematic diagram showing a north velocity error comparison between the biaxial rotational inertial navigation before and after dynamic error compensation. Comparing the two figures, it can be seen that under the condition of uncompensated secondary nonlinear parameters of the accelerometer and errors of lever arms in the accelerometer, the 180-degree steering of the biaxial rotational inertial navigation leads to a speed error of about 0.025m/s in the east direction and the north direction, and after the calibration compensation is carried out by adopting the method provided by the invention, the speed error caused by the dynamic state is obviously reduced, and the effect can reach 90%;

FIG. 4 (a) is a schematic diagram showing a comparison of east position errors before and after dynamic error compensation of the biaxial rotational inertial navigation system; fig. 4 (b) is a schematic diagram showing a north position error comparison between the biaxial rotational inertial navigation before and after dynamic error compensation. As can be seen from the comparison of the two figures, the comparison of the secondary nonlinear parameter of the uncompensated accelerometer, the error of the inner rod arm of the accelerometer and the position error of the navigation result obtained by the method can be seen, and in the navigation environment in short voyage, the positioning accuracy of the biaxial rotation inertial navigation in the dynamic environment can be improved by about 8 meters by the method provided by the invention.

In summary, the above experiments prove that the method for inhibiting the dynamic error of the biaxial rotation inertial navigation provided by the invention has the advantages of correctness and accuracy, good effect of inhibiting the dynamic error of the biaxial rotation inertial navigation, and good practicability.

Portions of the invention not disclosed in detail are well within the skill of the art. Although illustrative embodiments of the present invention have been described above to facilitate the 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, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims.

Claims

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

s1, constructing a gyroscope sensitive shaft system, an accelerometer sensitive shaft system, an IMU coordinate system, a geocentric inertial coordinate system, a terrestrial coordinate system and a navigation coordinate system, and determining an installation error matrix of a gyroscope and an installation error matrix of an accelerometer;

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

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 a Kalman filtering estimation result; wherein, the state quantity of the thirty-six-dimensional Kalman filter comprises an attitude error angle of the biaxial rotation inertial navigation

Speed error delta V, position error delta P, calibration parameter error X of gyro_gError X of calibration parameter of accelerometer_aCalibration error X of second-order nonlinear coefficient of accelerometer_Ka2Error of inner rod arm X_r；

S4, calibration test: after the preheating of the starting machine is finished, the double-shaft indexing mechanism rotates according to a designed indexing path, and angular rate data output by a gyroscope and specific force data output by an accelerometer of double-shaft rotational inertial navigation in the process are stored as calibration data; wherein, the transposition path should be designed to satisfy: each shaft of the double-shaft rotation inertial navigation inertial measurement unit rotates for 180 degrees in a single direction, and each shaft of the inertial measurement unit passes through two positions of pointing to the sky and pointing to the ground;

s5, processing the calibration data in 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 from an initial value along with the multiple transposition of the step S4, and finally the state quantity estimated value in the Kalman filter is obtained; wherein, the initial value of the thirty-six-dimensional state quantity is assigned based on the initial alignment result of the biaxial rotation and the instrument parameters; in the state quantity estimated value in the optimal Kalman filter, a state quantity component related to the error of the inertial device is a calibration parameter;

2. The method for suppressing the dynamic error of the biaxial rotational inertial navigation system according to claim 1, wherein the step S1 is implemented by:

s101, constructing a gyro sensitive axis system, namely a g system, wherein the coordinate system takes the measuring central points of three gyros as the origin of coordinates, the Xg axis is consistent with the sensitive axis direction of the X-direction gyro, the Yg axis is consistent with the sensitive axis direction of the Y-direction gyro, and the Zg axis is consistent with the sensitive axis direction of the Z-direction gyro;

in the formula (I), the compound is shown in the specification,

is a mounting error matrix of the gyro, gamma_yz、γ_zyAnd gamma_zxFor three mounting error angles of the gyro-sensitive axis system relative to the IMU coordinate system, in particular gamma_yzIndicating the angle of deflection, gamma, of the Y-axis gyro sensitive axis Yg about the Zm-axis of the m-system_zyIndicating the angle of deflection, gamma, of the Z-axis of gyro sensitivity Zg about the Ym-axis of the m-system_zxThe deflection angle of a Z-direction gyro sensitive axis Zg around an Xm axis of an m system is represented;

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

in the formula (I), the compound is shown in the specification,

is a mounting error matrix of the accelerometer, alpha_xz、α_xy、α_yz、α_yx、α_zyAnd alpha_zxFor six mounting error angles of the accelerometer sensitive axis system relative to the IMU coordinate system, in particular, alpha_xzRepresenting the deflection angle, alpha, of the sensitive axis Xa of the X-direction accelerometer about the Zm axis of the m-system_xyRepresenting the angle of deflection, alpha, of the sensitive axis Xa of the X-direction accelerometer about the Ym axis of the system m_yzThe deflection angle alpha of the sensitive axis Ya of the Y-direction accelerometer around the Zm axis of the m system_yxRepresenting the angle of deflection, alpha, of the sensitive axis Ya of the Y-direction accelerometer about the Xm axis of the m-system_zyRepresenting the deflection angle, alpha, of the axis Za of the sensitive axis of the Z-direction accelerometer about the Ym axis of the m-system_zxThe deflection angle of the sensing axis Za of the Z-direction accelerometer around the Xm axis of the m system is shown.

3. The method for suppressing the dynamic error of the biaxial rotational inertial navigation system according to claim 2, wherein the step S2 is implemented by:

an error equation of the biaxial rotational inertial navigation in a navigation coordinate system has the expression as follows:

in the formula (I), the compound is shown in the specification,

is composed of

The derivative with respect to time is determined,

is the attitude error angle of the biaxial rotational inertial navigation,

and

n is the rotation angular rate relative to i, which is generated by earth rotation and carrier motion;

for resolving navigation

The estimated error of (2);

a coordinate transformation matrix from an m system to an n system;

is the measurement error of the gyroscope;

is delta VⁿDerivative with respect to time, δ VⁿIs the velocity error, delta V, of the biaxial rotational inertial navigationⁿ＝[δV_E δV_N δV_U]^T，δV_E、δV_NAnd δ V_UEast-direction speed error, north-direction speed error and sky-direction speed error respectively; f. ofⁿIs a specific force under n series;

is the earth rotation angular rate;

is composed of

The error of (2);

is composed of

An error of (2); δ f^mIs the measurement error of the accelerometer;

is the accelerometer inner arm error; δ g is the gravity vector error;

is the derivative of δ L with respect to time, δ L being the latitude error;

is the derivative of δ λ with respect to time, δ λ is the longitude error;

is the derivative of δ h with respect to time, δ h being the height error; l, lambda and h are local geographic latitude, longitude and altitude, respectively; r is_MAnd R_NThe radiuses of the local earth meridian circle and the prime unit circle are respectively;

wherein the measurement error of the gyroscope

The expression of (a) is:

in the formula (I), the compound is shown in the specification,

and

respectively, X-direction gyro scale factors

Y-direction gyro scale factor

And Z-direction gyro scale factor

The error of (2); delta gamma_yz、δγ_zyAnd δ γ_zxRespectively a gyro installation error angle gamma_yz、γ_zyAnd gamma_zxThe error of (2);

ε^mthe zero offset error of the gyroscope is expressed as:

ε^m＝[ε_x ε_y ε_z]^T，

in the formula, epsilon_x、ε_yAnd epsilon_zZero offset errors of an X-direction gyroscope, a Y-direction gyroscope and a Z-direction gyroscope are respectively;

measurement error δ f of accelerometer^mThe expression of (a) is:

in the formula (I), the compound is shown in the specification,

and

scale factors for X-direction accelerometers respectively

Scale factor of Y-direction accelerometer

And Z-direction accelerometer scale factor

An error of (2); delta alpha_xz、δα_xy、δα_yz、δα_yx、δα_zyAnd delta alpha_zxRespectively an accelerometer mounting error angle alpha_xz、α_xy、α_yz、α_yx、α_zyAnd alpha_zxAn error of (2); delta K_A2Is a calibration error matrix of second order nonlinear coefficients of the accelerometer,

δK_ax2、δK_ay2and δ K_az2Respectively, the second-order nonlinear coefficient K of the X-direction accelerometer_ax2Calibration error of (2), second order of (Y) direction accelerometerCoefficient of non-linearity K_ay2Calibration error of the accelerometer and second-order nonlinear coefficient K of the accelerometer in Z direction_az2The calibration error of (2);

is the zero offset error of the accelerometer,

and

accelerometer inner lever arm error

The expression of (a) is:

in the formula (I), the compound is shown in the specification,

and

respectively error of inner rod arm

wherein the content of the first and second substances,

and

respectively measured values of the gyroscope in the m system

At X_mAxis, Y_mAxis and Z_mA component on the axis; delta r_x、δr_yAnd δ r_zRespectively an X-direction accelerometer inner lever arm r_xInner lever arm r of Y-direction accelerometer_yAnd Z-direction accelerometer inner lever arm r_zThe error of (2).

4. The method for suppressing the dynamic error of the biaxial rotational inertial navigation system according to claim 3, wherein the step S3 is implemented by the following steps:

In the formula,

is the attitude error angle of the biaxial rotational inertial navigation,

X_afor the error in the calibration parameters of the accelerometer,

in the formula (I), the compound is shown in the specification,

at F³³Each non-zero matrix element is:

F³⁶in the step (1), the first step,

G³⁶to measure the noise the input matrix is,

u is the noise of the measurement and is,

s303, constructing an observation equation of the thirty-six-dimensional Kalman filter:

Z＝H³⁶X³⁶+v，

wherein Z is an observed quantity, and when the biaxial rotational inertial navigation is kept in a stationary state during calibration with speed as an observed quantity, Z = [ V ]_EV_N V_U]^T；H³⁶To observe the matrix, H³⁶＝[0_3×3 I₃ 0_3×30]，I₃In an identity matrix of three rows and three columns, i.e.

in the formula (I), the compound is shown in the specification,

is composed of

The anti-symmetric matrix of (a) is,

for biaxial rotary inertial navigation

Calculating the result of (1);

v for biaxial rotational inertial navigationⁿCalculating the result of (1);

the calculation result is the L of the biaxial rotation inertial navigation;

the calculation result is the h of the biaxial rotation inertial navigation; ,

k before feedback compensation for Kalman filtering estimation result_G；

Compensating for Kalman filter estimation result feedbackEpsilon before compensation^m；，

K before feedback compensation for Kalman filtering estimation result_A；

Before feedback compensation for Kalman filtering estimation result

K before feedback compensation for Kalman filtering estimation result_A2；

R before feedback compensation for Kalman filter estimation results_x；

R before feedback compensation for Kalman filter estimation results_y；

R before feedback compensation for Kalman filtering estimation results_z。

5. The method for suppressing the dynamic error of the biaxial rotational inertial navigation system according to claim 1, wherein in step S4, the indexing path of the biaxial indexing mechanism is specifically designed to:

initial positions are corresponded based on the order 0: standing the biaxial rotary inertial navigation in postures that the Xm axis faces east, the Ym axis faces north and the Zm axis faces sky for 10 minutes;

sequence 1: clockwise rotating by 90 degrees by taking the middle frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face east, sky, and south, respectively; after the transposition is finished, standing for 180s;

sequence 4: clockwise rotates 90 degrees by taking the inner frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation face the sky, the Ym axis, and the Zm axis, respectively; after transposition is completed, standing for 180s;

sequence 8: clockwise rotating 180 degrees by taking the middle frame shaft as a rotating shaft; in the state, the Xm axis, the Ym axis and the Zm axis of the biaxial rotation inertial navigation face the north direction, the Ym axis faces the west direction and the Zm axis faces the sky direction respectively; after transposition is completed, standing for 180s;

sequence 9: clockwise rotating 180 degrees by taking the middle frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face south, west, and ground, respectively; after the transposition is finished, standing for 180s;

sequence 10: clockwise rotating by 90 degrees by taking the middle frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face the ground, the Ym axis, and the Zm axis, respectively, face the west; after the transposition is finished, standing for 180s;

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

sequence 13: clockwise rotates 90 degrees by taking the inner frame shaft as a rotating shaft; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotary inertial navigation system face the west, the Ym axis, and the earth, respectively; after the transposition is finished, standing for 180s;

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

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

sequence 17: the middle frame shaft is taken as a rotating shaft and rotates 90 degrees clockwise; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face east, ground, and north, respectively; after the transposition is finished, standing for 180s;

sequence 18: the middle frame shaft is taken as a rotating shaft and rotates 90 degrees clockwise; in this state, the Xm axis, the Ym axis, and the Zm axis of the biaxial rotational inertial navigation system face east, north, and sky, respectively; after indexing is completed, rest is carried out for 180s.

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

7. The method for suppressing the dynamic error of the biaxial rotational inertial navigation system according to claim 3, wherein the step S5 is implemented by:

s501, carrying out initial value assignment on the 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; assigning the initial value of the delta P by a difference value obtained by subtracting an actual experiment position from an initial position output after the initial alignment is completed by the biaxial rotational inertial navigation in the step S4; x_g、X_a、X_Ka2And X_rThe initial value of (A) is assigned according to the actual conditions of the gyroscope and the accelerometer in the biaxial rotational inertial navigation;

Y-direction gyro scale factor

And Z-direction gyro scale factor

Zero bias of Y-direction gyroscope

Zero-offset with Z-direction gyro

Scale factor of X-direction accelerometer

Scale factor of Y-direction accelerometer

And Z-direction accelerometer scale factor

Zero offset of Y-direction accelerometer

And zero offset of Z-direction accelerometer

Inner lever arm r of X-direction accelerometer_xY-direction addendum meter inner lever arm r_yAnd an inner lever arm r of the Z-direction accelerometer_z。

8. The method for suppressing the dynamic error of the biaxial rotational inertial navigation system according to claim 7, wherein the step S6 is implemented by:

s601, adopting the existing sixty-fourAnd the sequence rotation modulation scheme is used as an indexing mechanism rotation scheme in the biaxial rotation inertial navigation process, and stops for 10s after each rotation to a position to obtain the rotation-modulated output result of the inertial device, including the angular rate of gyroscope output

And specific force output by accelerometer

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

in the formula (I), the compound is shown in the specification,

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

in the formula (I), the compound is shown in the specification,

s603, utilizing the output after the gyroscope calibration and the output after the accelerometer calibration obtained in the step S602, and utilizing an inner lever arm r of the X-direction accelerometer_xInner lever arm r of Y-direction accelerometer_yAnd an inner lever arm r of the Z-direction accelerometer_zThe acceleration data is compensated in real time, and the specific formula is as follows:

in the formula, a_xb、a_ybAnd a_zbThe components of the real-time acceleration result after the compensation of the inner rod arm of the accelerometer on the Xm axis, the Ym axis and the Zm axis in the m system are obtained; a is a_xc、a_ycAnd a_zcThe components of an Xm axis, a Ym axis and a Zm axis in an m system of an acceleration real-time result before the compensation of an inner rod arm of the accelerometer is performed; omega_xc、ω_ycAnd ω_zcThe components of the angular velocity in the m system are Xm axis, ym axis and Zm axis;

s604, converting a in the step S603_xb、a_yb、a_zbAnd ω_xc、ω_yc、ω_zcAnd (4) bringing an inertial navigation resolving equation into the inertial navigation system, and obtaining a navigation result of the biaxial rotation inertial navigation system through resolving, namely the navigation result obtained after real-time compensation is carried out on the dynamic error of the biaxial rotation inertial navigation system.