CN101907638A

CN101907638A - Method for calibrating accelerometer under unsupported state

Info

Publication number: CN101907638A
Application number: CN 201010205033
Authority: CN
Inventors: 张海; 毛友泽; 沈晓蓉; 任章
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2010-06-11
Filing date: 2010-06-11
Publication date: 2010-12-08
Anticipated expiration: 2030-06-11
Also published as: CN101907638B

Abstract

The invention discloses a method for calibrating an accelerometer under an unsupported state, which is applied to an inertial navigation system with the capacity of initially aligning with a static base attitude. The method comprises the following steps of: firstly, simplifying an error model, repeatedly changing the carrier position, and coarsely and finely aligning with each position by using the static base to acquire the attitude information; and calculating the three-axis component of an acceleration of gravity g projected under a carrier coordinate system according to the attitude information, and recording the measured value of the accelerometer at each position. The invention provides a 10-position calibrating scheme, which comprises the following steps of: acquiring zero offset to degenerate the error model into a linear model by identifying the zero offset through a nonlinear least square method according to the calculated value and measured value of the projected component; and mounting an error and scale factor coupled matrix by identifying through a linear least square method. Therefore, the key parameters of the accelerometer are calibrated. The method has the advantages of capacities of realizing unsupported calibration of the accelerometer and effectively estimating the key parameters of the accelerometer with time-varying performance, along with simple process and high speed.

Description

Method for calibrating accelerometer in unsupported state

Technical Field

The invention belongs to the technical field of inertial navigation, and particularly relates to a method for calibrating an accelerometer in an unsupported state.

Background

The accelerometer is effectively calibrated, so that the problem of time-varying performance parameters of the accelerometer can be solved, and the improvement of the measurement precision is very necessary. The traditional calibration method needs calibration equipment such as a rotary table and a centrifuge to carry out complete system-level calibration on unknown parameters, has high calibration precision, but has complex operation, long calibration period and poor real-time performance; therefore, the concept of accelerometer calibration in an unsupported state is provided for the problems, namely calibration can be realized on the use site only by means of an inertia device and without depending on laboratory conditions, and generally only parameters with the most serious influence on the performance of the accelerometer are identified due to the limitation on the site calibration conditions, so that fewer documents are published for accelerometer unsupported site calibration at present.

The method has the advantages of simple structure, time saving and easy realization compared with a multi-position method, but can not calibrate installation errors and scale factor errors, and is only suitable for a short-time low-medium-precision navigation system.

A six-position rotation field calibration method is provided for an optical fiber gyroscope IMU (inertial measurement Unit) by Liubaiqi and House construction of Beijing aerospace university, twelve rotations are performed on six positions by means of a horizontal plane, 42 nonlinear input and output equations are established, and inertial device parameter calibration is performed by rotation integral and symmetrical position error cancellation.

The identification scheme based on the optimization of the downhill simple is provided by W T Fong, S K Ong and A Y C Nee of the national university of Singapore, the operation is simple, and complete error parameters can be identified.

Disclosure of Invention

In order to solve the problems that the installation error and scale factor error of the accelerometer cannot be marked or identified and the identification result precision is low, the invention provides the method for calibrating the accelerometer in the unsupported state

(\begin{matrix} g_{xa} \\ g_{ya} \\ g_{za} \end{matrix}) = (\begin{matrix} K_{11} k_{x} & K_{12} k_{y} & K_{13} k_{z} \\ K_{21} k_{x} & K_{22} k_{y} & K_{23} k_{z} \\ K_{31} k_{x} & K_{32} k_{y} & K_{33} K_{z} \end{matrix}) (\begin{matrix} (g_{xm} - g_{x 0}) \\ (g_{ym} - g_{y 0}) \\ (g_{zm} - g_{z 0}) \end{matrix}) - - - (1)

In the formula, k_x、k_y、k_zScale factors for x, y, z axes of the accelerometer; k₁₁，K₁₂，K₁₃，K₂₁，K₂₂，K₂₃，K₃₁，K₃₂，K₃₃Is an installation error matrix element; g_x0、g_y0、g_z0Zero offset of x, y and z axes of the accelerometer; g_xm、g_ym、g_zmAre accelerometer x, y, z axis measurements; g_xa、g_ya、g_zaThe gravity acceleration g is a projection component under a carrier coordinate system;

is a coupling matrix of mounting errors and scale factors.

Calibration is further accomplished by 5 steps:

step 1: roughly aligning the static base to obtain a roll angle gamma and a pitch angle theta of the carrier;

step 2: the Kalman filtering is utilized to carry out precise alignment on the static base, the alignment precision of the roll angle gamma and the pitch angle theta is improved, and the calculated value (g) of the three-axis component of the projection of the gravity acceleration g in a carrier coordinate system is further obtained_xa，g_ya，g_za)；

And step 3: the carrier is carried out on 10 different positions in step 1 and step 2 to obtain 10 groups of accelerometer x, y and z axis measurement values (g)_xm，g_ym，g_zm) And 10 sets of calculation values (g) of three-axis components of the projection of the gravity acceleration g in the carrier coordinate system_xa，g_ya，g_za). In the step, the process is judged according to whether the carriers are placed on 10 positions, if not, the process is switched to the step 1, and if the process is completed, the required data is obtained, and the step 4 is continued.

And 4, step 4: obtaining zero offset g of accelerometer by nonlinear least square method_x0，g_y0，g_z0；

And 5: by linear optimizationMultiplying by two to obtain a coupling matrix

Obtaining the zero deviation g in the step 4_x0，g_y0，g_z0And substituting the values of the coupling matrix in the step 5 into the formula (1) to construct an error model of the formula (1). So that the accelerometer measurements g can be measured_xm，g_ym，g_zmEffective correction is carried out to obtain the projection component g of the corrected gravity acceleration g under the carrier coordinate system_xa，g_ya，g_zaThereby improving the accuracy of the measurement.

The invention has the advantages that:

(1) the accelerometer can be calibrated without depending under the external field condition, the accelerometer is separated from the laboratory condition, and the traditional calibration equipment is not used;

(2) the calibration process is simple, the calibration speed is high, the accelerometer can be calibrated before being used every time, and the problem of time-varying performance parameters is effectively solved.

(3) The application of the nonlinear least square method can solve the problem of nonlinearity of an error model, avoid the dependence of the traditional calibration on calibration equipment such as a turntable and the like, and realize the calibration of the accelerometer in a non-dependence state.

Drawings

FIG. 1 is a flow chart of the steps of the calibration method of the present invention.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings.

Before calibration, the error model of the triaxial accelerometer needs to be simplified:

on the premise of field calibration, only the error parameter which has the most serious influence on the performance of the accelerometer is considered, and the error model of the triaxial accelerometer can be simplified as follows:

(\begin{matrix} g_{xa} \\ g_{ya} \\ g_{za} \end{matrix}) = (\begin{matrix} K_{11} & K_{12} & K_{13} \\ K_{21} & K_{22} & K_{23} \\ K_{31} & K_{32} & K_{33} \end{matrix}) (\begin{matrix} k_{x} (g_{xm} - g_{x 0}) \\ k_{y} (g_{ym} - g_{y 0}) \\ k_{z} (g_{zm} - g_{z 0}) \end{matrix}) - - - (1)

in the formula,

to install the error matrix, K₁₁、K₁₂、K₁₃、K₂₁、K₂₂、K₂₃、K₃₁、K₃₂And K₃₃Is an installation error matrix element; k is a radical of_x、k_y、k_zScale factors for x, y, z axes of the accelerometer; g_x0、g_y0、g_z0Zero offset of x, y and z axes of the accelerometer; g_xm、g_ym、g_zmAre accelerometer x, y, z axis measurements; g_xa、g_ya、g_zaThe calculated value of the projection component of the gravity acceleration g in the carrier coordinate system is shown.

Further simplification of formula (1) and yields:

(\begin{matrix} g_{xa} \\ g_{ya} \\ g_{za} \end{matrix}) = (\begin{matrix} K_{11} k_{x} & K_{12} k_{y} & K_{13} k_{z} \\ K_{21} k_{x} & K_{22} k_{y} & K_{23} k_{z} \\ K_{31} k_{x} & K_{32} k_{y} & K_{33} K_{z} \end{matrix}) (\begin{matrix} (g_{xm} - g_{x 0}) \\ (g_{ym} - g_{y 0}) \\ (g_{zm} - g_{z 0}) \end{matrix}) - - - (2)

wherein,

is a coupling matrix S of mounting errors and scale factors.

The coupling matrix S of mounting errors and scale factors is expressed in a simplified manner as follows:

S = (\begin{matrix} S_{11} & S_{12} & S_{13} \\ S_{21} & S_{22} & S_{23} \\ S_{31} & S_{32} & S_{33} \end{matrix}) - - - (3)

wherein, the elements in the matrix shown in the formula (3) correspond to the elements in the coupling matrix of the installation error and the scale factor in the formula (2) one by one;

the invention relates to a method for calibrating an accelerometer in an unsupported state, which comprises the following steps of calibrating the accelerometer by the following 5 steps:

step 1: and (5) roughly aligning the static base to obtain a roll angle gamma and a pitch angle theta of the carrier. In the embodiment of the invention, the alignment errors of the roll angle gamma and the pitch angle theta of the carrier are controlled within 1 degree, and the roll angle gamma and the pitch angle theta of the carrier are obtained by the following process.

By:

(\begin{matrix} g_{x}^{b} \\ g_{y}^{b} \\ g_{z}^{b} \end{matrix}) = C_{n}^{b} (\begin{matrix} g_{x}^{n} \\ g_{y}^{n} \\ g_{z}^{n} \end{matrix}) - - - (4)

obtaining a direction cosine matrix between a carrier coordinate system and a geographic coordinate system of the carrier:

wherein,

the three-axis component measurement value of the gravity acceleration g projected under the carrier coordinate system is obtained;

the three-axis component of the gravity acceleration g projected under the geographic coordinate system; omega_ieThe angular velocity of the earth rotation is a constant with the value of 7.292115147e-5 radians per second;

three-axis components of the projection of the rotational angular velocity of the earth in a carrier coordinate system are obtained;

three-axis components of the earth rotation angular velocity projected under a geographic system; l is the local geographical latitude; g is the local gravitational acceleration.

The direction cosine matrix in equation (6) is represented in a simplified manner as follows:

C_{n}^{b} = [\begin{matrix} T_{11} & T_{12} & T_{13} \\ T_{21} & T_{22} & T_{23} \\ T_{31} & T_{32} & T_{33} \end{matrix}] - - - (7)

wherein, the elements in the matrix shown in the formula (7) correspond to the elements in the matrix shown in the formula (6) one by one;

thus, the pitch angle θ and the roll angle γ with a carrier error within 1 ° can be obtained from equation (7):

θ＝sin^-1T₂₃ (8)

γ＝tg^-1(-T₁₃/T₃₃) (9)

step 2: and carrying out precise alignment on the static base by using Kalman filtering, improving the alignment precision of the roll angle gamma and the pitch angle theta, and obtaining the pitch angle theta 'and the roll angle gamma'.

In the embodiment of the invention, the alignment error of the carrier is within 50 arc seconds, and the process of specifically obtaining the pitch angle theta 'and the roll angle gamma' is as follows.

Applying Kalman filtering to the precise alignment of the static base, wherein the Kalman filtering state equation is as follows:

the Kalman filter measurement equation is:

wherein phi is_x、φ_y、φ_zRespectively a carrier pitching error angle, a carrier rolling error angle and a carrier course error angle; epsilon_x、ε_y、ε_zRespectively installing x, y and z axial gyro errors of a coordinate system for the carrier;

respectively installing errors of an x-axis accelerometer and a y-axis accelerometer of a coordinate system for the carrier; delta V_x、δV_yRespectively installing x and y axial carrier speed errors of a coordinate system for the carrier; r is the radius of the earth; eta_x、η_yRespectively installing speed noises of x and y axes of a coordinate system for the carrier; and L is the local geographical latitude.

Phi can be obtained by the following formulas (10) and (11)_x、φ_y、φ_z、ε_x、ε_y、ε_z、

δV_x、δV_y。

By phi_x、φ_y、φ_zAn error matrix, let it be C, is formed, as follows:

then the direction cosine matrix after fine alignment can be obtained

The direction cosine matrix after fine alignment

Expressed in a simplified manner as follows:

wherein, the direction cosine matrix after the elements in the matrix shown in the formula (14) are precisely aligned with the formula (13)

The middle elements correspond one to one. This can be obtained by the formula (14):

θ′＝sin^-1T′₂₃ (15)

γ′＝tg^-1(-T′₁₃/T′₃₃) (16)

thereby obtaining the pitch angle theta 'and the roll angle gamma' of the carrier alignment error within 50 arc seconds. Projecting the gravity acceleration g to a carrier coordinate system to obtain a calculated value of a projected triaxial component of the gravity acceleration g in the carrier coordinate system:

g_xa＝-sin(γ′)·cos(θ′)·g (17)

g_ya＝sin(θ′)·g (18)

g_za＝cos(γ′)·cos(θ′)·g (19)

and step 3: placing a carrier at 10 different positions, wherein the coarse alignment and the precise alignment of the static base in the step 1 and the step 2 are required to be carried out at each position, judging whether the placement of the 10 positions is finished, if not, turning to the step 1, and if so, obtaining the x-axis, y-axis and z-axis measurement values (g) of 10 groups of accelerometers_xm，g_ym，g_zm) And 10 sets of calculation values (g) of three-axis components of the projection of the gravity acceleration g in the carrier coordinate system_xa，g_ya，g_za)。

And 4, step 4: obtaining zero offset g of accelerometer by nonlinear least square method_x0，g_y0，g_z0。

a. Constructing an objective function;

the equation (2) can be modified according to the equation (3) to make the objective function

f(p)＝[S₁₁(g_xm-g_x0)+S₁₂(g_ym-g_y0)+S₁₃(g_zm-g_z0)]²+[S₂₁(g_xm-g_x0)+S₂₂(g_ym-g_y0)+S₂₃(g_zm-g_z0)]² (20)

+[S₃₁(g_xm-g_x0)+S₃₂(g_ym-g_y0)+S₃₃(g_zm-g_z0)]²-(g_xp ²+g_yp ²+g_zp ²)

Wherein p ═ g_x0，g_y0，g_z0，S₁₁，S₁₂，S₁₃，S₂₁，S₂₂，S₂₃，S₃₁，S₃₂，S₃₃]；

b. Solving a Jacobian matrix of the objective function f (p);

the jacobian matrix J of the objective function f (p) is:

in the formula (f)₁...f₁₀Is an objective function f (p) at the 1 st to 10 th positions; p is a radical of₁...p₁₂The 1 st to 12 th elements of the vector p.

c. Iteratively approximating an unknown vector p;

solving the equation:

obtaining the k step correction quantity delta of the vector p^(k)。

Wherein, J_kUpdates the k-th step of the jacobian matrix J,is J_kTransposing; v. of_kIs an adjustable iteration step length; i is a 12-order unit array;

is the updated result of the k step of the objective function f (p) at the 1 st to 10 th positions;

by passing

p^(k+1)＝p^(k)+δ^(k) (23)

In the formula, p^(k+1)Updating the k +1 step of the p vector; p is a radical of^(k)Updating the value of the k step for the p direction; the solution iteration is repeated for equations (20), (21), (22), (23) until the vector p converges to a stable value. The first three elements g of the vector p_x0，g_y0，g_z0I.e. the zero offset of the accelerometer.

And 5: obtaining a coupling matrix S through a linear least square method;

the zero deviation g obtained in the step 4 is compared_x0，g_y0，g_z0The formula (2) is taken in, the error model of the formula (2) can be degenerated into linearity, and a coupling matrix S can be obtained by using a linear least square method, wherein the coupling matrix S is as follows:

S＝(R*(G^T*(G*G^T)^-1))^-1 (25)

wherein:

G = (\begin{matrix} g_{xa 1} & . . . & g_{xa 10} \\ g_{ya 1} & . . . & g_{ya 10} \\ g_{za 1} & . . . & g_{za 10} \end{matrix});

G^Tis the transpose of G;

R = (\begin{matrix} g_{xm 1} - g_{x 0} & . . . & g_{xm 10} - g_{x 0} \\ g_{ym 1} - g_{y 0} & . . . & g_{ym 10} - g_{y 0} \\ g_{zm 1} - g_{z 0} & . . . & g_{zm 10} - g_{z 0} \end{matrix})

in the formula, g_xa1...g_xa10，g_ya1...g_ya10，g_za1...g_za10The projection of the gravity acceleration g under the carrier coordinate system under the 1 st to the 10 th positions; g_xm1...g_xm10，g_ym1...g_ym10，g_zm1...g_zm10Are the x, y, z axis measurements of the accelerometer in the 1 st to 10 th positions.

Obtaining the zero deviation g in the step 4_x0，g_y0，g_z0And the value of the coupling matrix S of the installation error and the scale factor in the step 5 is substituted into the formula (2), so that an error model of the formula (2) can be constructed, and the measurement value g of the accelerometer can be measured_xm，g_ym，g_zmEffective correction is carried out to obtain the projection component g of the corrected gravity acceleration g under the carrier coordinate system_xa，g_ya，g_zaThereby improving the accuracy of the measurement.

The non-linear least squares and the linear least squares performed in the above steps 4 and 5 require that the correlation among the 10 positions of the carrier in the steps 1 and 2 is small, i.e., 10 groups (g)_xa，g_ya，g_za) 10 groups (g)_xm，g_ym，g_zm) The correlation between them is small. The present invention employs the following position selection method (different pitch and roll represent different positions) as shown in table 1.

Table 110 location selection scheme one

Attitude angle	1	2	3	4	5	6	7	8	9	10
											Pitch angle/(°)	0	-20	40	-60	80	-100	120	-140	160	-180

Roll angle/(°)

-10

30

-50

70

-90

110

-130

150

-170

10

The scheme meets the requirement of correlation, and the calibration precision is high under the selection method. The simulation verification for this location scheme is as follows: and (3) carrying out calibration experiments according to the position scheme through MATLAB programming verification of mathematical software, wherein if parameters such as zero offset and the like can be accurately identified, 10 calibration positions are irrelevant, and otherwise, the operation is not relevant. In the verification process, 3000 experiments are performed, the number of experiments in which the parameters to be solved can be accurately identified is recorded as an evaluation index of the scheme, different 10-position schemes are selected for comparison, and the result is shown in table 5.

The 10 position was chosen as follows for scheme two of table 2:

table 210 position selection scheme two

Attitude angle	1	2	3	4	5	6	7	8	9	10
											Pitch angle/(°)	0	-20	40	-60	80	-100	120	-140	160	-180
Roll angle/(°)	0	30	-50	70	-90	110	-130	150	-170	10

The 10 position was selected as follows for scheme three of table 3:

table 310 position selection scheme three

Attitude angle	1	2	3	4	5	6	7	8	9	10
											Pitch angle/(°)	0	-20	40	-60	80	-100	120	-140	160	-180
Roll angle/(°)	-10	10	-30	50	-70	90	-110	130	-150	170

The 10 position was chosen as follows for scheme four of table 4:

table 410 position selection scheme four

Attitude angle	1	2	3	4	5	6	7	8	9	10
											Pitch angle/(°)	0	-20	40	-60	80	-100	120	-140	160	-180
Roll angle/(°)	0	-30	50	-70	90	-110	130	-150	170	-10

The 10-position selection is performed in four schemes, each of which performs 3000 experiments, and the statistical results of the experiment times for which the parameters to be solved can be accurately identified in each scheme are shown in table 5:

TABLE 5 comparative results

As can be seen from table 5, the 10-position selection has the highest number of experiments for accurately identifying the parameter to be solved in the case of the first scheme, and thus the first scheme is selected as the preferred scheme.

Claims

1. A method for calibrating an accelerometer in an unsupported state is characterized in that: before the calibration process, firstly, the error parameter which has the most serious influence on the performance of the accelerometer needs to be considered, and the error model of the simplified triaxial accelerometer is as follows:

(\begin{matrix} g_{xa} \\ g_{ya} \\ g_{za} \end{matrix}) = (\begin{matrix} K_{11} k_{x} & K_{12} k_{y} & K_{13} k_{z} \\ K_{21} k_{x} & K_{22} k_{y} & K_{23} k_{z} \\ K_{31} k_{x} & K_{32} k_{y} & K_{33} k_{z} \end{matrix}) (\begin{matrix} (g_{xm} - g_{x 0}) \\ (g_{ym} - g_{y 0}) \\ (g_{zm} - g_{z 0}) \end{matrix}) - - - (1)

wherein k is_x、k_y、k_zScale factors for x, y, z axes of the accelerometer; k₁₁、K₁₂、K₁₃、K₂₁、K₂₂、K₂₃、K₃₁、K₃₂And K₃₃Is an installation error matrix element; g_x0、g_y0、g_z0Zero offset of x, y and z axes of the accelerometer; g_xm、g_ym、g_zmAre accelerometer x, y, z axis measurements; g_xa、g_ya、g_zaThe calculated value of the projection component of the gravity acceleration g under the carrier coordinate system is obtained;

a coupling matrix of mounting errors and scale factors;

further calibration is accomplished by the following 5 steps:

step 2: the Kalman filtering is utilized to carry out precise alignment on the static base, the alignment precision of the roll angle gamma and the pitch angle theta is improved, and the calculated value (g) of the three-axis component of the projection of the gravity acceleration g under the carrier coordinate system is obtained_xa，g_ya，g_za)；

And step 3: placing the carrier at 10 different positions to perform the steps 1 and 2, judging whether the placement at 10 positions is finished, if not, executing the step 1, and if so, obtaining the x-axis measurement value, the y-axis measurement value and the z-axis measurement value (g) of 10 groups of accelerometers_xm，g_ym，g_zm) And 10 sets of calculation values (g) of three-axis components of the projection of the gravity acceleration g in the carrier coordinate system_xa，g_ya，g_za) Continuing to step 4;

and 4, step 4: obtaining triaxial zero offset g of accelerometer by nonlinear least square method_x0，g_y0，g_z0；

And 5: obtaining a coupling matrix of installation errors and scale factors by a linear least square method

(\begin{matrix} K_{11} k_{x} & K_{12} k_{y} & K_{13} k_{z} \\ K_{21} k_{x} & K_{22} k_{y} & K_{23} k_{z} \\ K_{31} k_{x} & K_{32} k_{y} & K_{33} k_{z} \end{matrix});

The zero deviation g obtained in the step 4 is compared_x0、g_y0、g_z0And substituting the values of the coupling matrix of the installation error and the scale factors into the formula (1), constructing an error model of the formula (1), and realizing the calibration of the accelerometer in an unsupported state.

2. The method for calibrating the accelerometer in the unsupported state as claimed in claim 1, wherein: and 4, obtaining the three-axis zero offset through a nonlinear least square method, and specifically comprising the following steps:

step a, constructing a target function;

transforming equation (1) into the order of the objective function f (p)

f(p)＝[K₁₁k_x(g_xm-g_x0)+K₁₂k_y(g_ym-g_y0)+K₁₃k_z(g_zm-g_z0)]²+[K₂₁k_x(g_xm-g_x0)+K₂₂k_y(g_ym-g_y0)+K₂₃k_z(g_zm-g_z0)]² (2)

+[K₃₁k_x(g_xm-g_x0)+K₃₂k_y(g_ym-g_y0)+K₃₃k_z(g_zm-g_z0)]²-(g_xa ²+g_ya ²+g_za ²)

Wherein, the vector p ═ g_x0，g_y0，g_z0，S₁₁，S₁₂，S₁₃，S₂₁，S₂₂，S₂₃，S₃₁，S₃₂，S₃₃]；

B, solving a Jacobian matrix of the objective function f (p);

the jacobian matrix J of the objective function f (p) is:

wherein f is₁...f₁₀Is an objective function f (p) at the 1 st to 10 th positions; p is a radical of₁...p₁₂Is given as vector p ═ g_x0，g_y0，g_z0，S₁₁，S₁₂，S₁₃，S₂₁，S₂₂，S₂₃，S₃₁，S₃₂，S₃₃]1 st to 12 th element of (1);

step c, iterative approximation is carried out on an unknown vector p;

solving the equation:

obtaining the k step correction quantity delta of the vector p^(k)；

Wherein, J_kUpdates the k-th step of the jacobian matrix J,

is J_kTransposing; v. of_kIs an adjustable iteration step length; i is a 12-order unit array;

by passing

p^(k+1)＝p^(k)+δ^(k) (5)

Wherein p is^(k+1)Updating the k +1 step of the vector p; p is a radical of^(k)Updating the value of the k step for the vector p; solving iterations for equations (2), (3), (4), (5) until vector p converges to a stable value; the first three elements g of the vector p_x0，g_y0，g_z0Is the null of the accelerometer.

3. The method for calibrating the accelerometer in the unsupported state as claimed in claim 1, wherein: and 5, obtaining the coupling matrix of the installation error and the scale factor by a linear least square method, and specifically comprising the following steps:

deviation of zero position g_x0，g_y0，g_z0Taking formula (1), degrading the error model of formula (1) into linearity, and obtaining the coupling matrix by using a linear least square method

Comprises the following steps:

(\begin{matrix} K_{11} k_{x} & K_{12} k_{y} & K_{13} k_{z} \\ K_{21} k_{x} & K_{22} k_{y} & K_{23} k_{z} \\ K_{31} k_{x} & K_{32} k_{y} & K_{33} k_{z} \end{matrix}) = {(R * (G^{T} * {(G * G^{T})}^{- 1}))}^{- 1} - - - (6)

wherein:

G = (\begin{matrix} g_{xa 1} & . . . & g_{xa 10} \\ g_{ya 1} & . . . & g_{ya 10} \\ g_{za 1} & . . . & g_{za 10} \end{matrix});

G^Tis the transpose of G;

R = (\begin{matrix} g_{xm 1} - g_{x 0} & . . . & g_{xm 10} - g_{x 0} \\ g_{ym 1} - g_{y 0} & . . . & g_{ym 10} - g_{y 0} \\ g_{zm 1} - g_{z 0} & . . . & g_{zm 10} - g_{z 0} \end{matrix})

in the formula, g_xa1...g_xa10，g_ya1...g_ya10，g_za1...g_za10The projection of the gravity acceleration g under the carrier coordinate system under the 1 st to the 10 th positions; g_xm1...g_xm10，g_ym1...g_ym10，g_zm1...g_zm10The x, y and z axis measurement values of the accelerometers of the carrier in the 1 st to 10 th positions are obtained.

4. The method for calibrating the accelerometer in the unsupported state as claimed in claim 1, wherein: the pitch angle and the roll angle were (0 °, -10 °), (-20 °, 30 °), (40 °, -50 °) (60 °, 70 °), (80 °, -90 °), (-100 °, 110 °), (120 °, -130 °), (-140 °, 150 °), (160 °, (170 °), (-180 °, 10 °) respectively, and 10 positions of the carrier were selected.