CN102393210A - Temperature calibration method of laser gyro inertia measurement unit - Google Patents

Abstract

The invention provides a method for accurately calibrating temperature error coefficients of a laser gyro inertia measurement unit. In the method, a three-axle table with a thermostate is utilized to enable an LIMU to achieve whole thermal balance through a measure of performing long-term heat preservation at a certain temperature spot; system inherent error coefficients such as a gyro scale factor, a gyro literal drift, an accelerometer scale factor, an accelerometer literal bias and the like at the temperature spot are accurately calibrated through a calibration method of combining dynamic rotation and static 24 position; and then high and low temperature cycling tests are performed on the LIMU by utilizing the inherent error coefficients of the LIMU at the temperature spot, so that the temperature error coefficients comprising 30 temperature related coefficients such as a primary temperature coefficient, a secondary temperature coefficient, a temperature gradient coefficient and a temperature change rate coefficient of the gyro literal drift and accelerometer literal bias are further calibrated. The method provided by the invention has the characteristics of high accuracy and simplicity in operation, and can be used for greatly improving the use accuracy of the LIMU under a variable temperature environment.

Description

The temperature calibration method of a kind of laser gyroscope inertia measurement unit

Technical field

(Laser Gyro InertialMeasurement Unit, the LIMU) method of temperature error coefficient can be used for the temperature calibration of laser gyroscope inertia measurement unit to the present invention relates to a kind of accurate Calibration of Laser gyroscopic inertia measuring unit.

Background technology

Laser gyro has short, characteristics such as dynamic range is big, reliability is high, the life-span is long, digital output start-up time as the desirable device of inertial navigation.In recent years, the laser gyro strap down inertial navigation system successfully applies to a plurality of fields such as Aeronautics and Astronautics, navigation in a large number.Laser gyroscope inertia measurement unit LIMU is the core component of laser gyro strap down inertial navigation system; Under many application scenarios, the environment temperature acute variation directly influences the variation of LIMU inherent error coefficient; Particularly gyroscope constant value zero partially and accelerometer often be worth biasing; To produce big ups and downs with temperature variation, thereby influence the precision of laser gyro and accelerometer output data, further influence the operating accuracy of inertial navigation system.Therefore, the laser gyro strap down inertial navigation before use must through temperature calibration test determine among the LIMU gyroscope constant value zero partially and accelerometer often be worth the temperature error coefficient of biasing, and in system, compensate.

Traditional LIMU temperature calibration method mainly is based on the constant temperature of many temperature spots and demarcates; The scaling method that this scaling method adopts dynamically rotation and static 24 positions to combine under the isoperibol of many group different temperature points; Obtain many group systems inherent error coefficient of the corresponding different temperature points of LIMU; Again systematic error and temperature are carried out linear fit, obtain corresponding temperature error coefficient.There are following two problems in this method: 1, the system temperature error is not thoroughly separated with the system inherent error, has the phase mutual interference; 2, only demarcate error under many groups steady temperature environment, do not demarcated the error under the temperature dynamic changing environment.Therefore, LIMU system inherent error coefficient and the temperature error coefficient precision of using this method to calibrate are limited, be not suitable for temperature fast, the practical applications occasion of acute variation.In the practical engineering application environment; The beginning of working from power on of laser gyroscope inertia measurement unit; Self temperature of gyro and accelerometer is in the change procedure all the time; The influence of the ambient temperature that is changed on the one hand receives the influence of gyro and accelerometer self work heating on the one hand, thereby makes gyro and accelerometer self form complicated temperature field from inside to outside; Have a strong impact on the measuring accuracy of laser gyro and accelerometer, further influenced the service precision of Inertial Measurement Unit.Simultaneously, traditional LIMU temperature calibration method obtains is temperature error model under the steady temperature environment of limited number temperature spot, need be through the method for sectional linear fitting the approximate continuous model that obtains, this has brought bigger approximate error for the temperature error model.

Summary of the invention

Technology of the present invention is dealt with problems and is: the deficiency that overcomes prior art; The high-precision temperature scaling method of a kind of laser gyroscope inertia measurement unit is provided; This method has the high and characteristics simple to operate of precision, has improved the service precision of LIMU under varying temperature environment greatly.

Technical solution of the present invention is: the temperature calibration method of a kind of laser gyroscope inertia measurement unit, and performing step is following:

(1) the laser gyroscope inertia measurement unit is installed on the three-axle table that has incubator, setting the interior temperature of incubator is T _MBe 20 ℃～30 ℃, insulation is 6～8 hours under LIMU works on power state;

(2) utilize three-axle table that LIMU is dynamically rotated rating test, rotate three-axle table and successively X axle, Y axle, the Z axle of LIMU are overlapped with the Z axle of turntable, all the other diaxons are in the surface level, make three-axle table with angular speed ω in each position ₀Respectively rotate 360 ° around clockwise, the counterclockwise both direction of the Z of geographic coordinate system axle, record LIMU output data;

(3) utilize the LIMU output data that is write down, according to the LIMU error mathematic model, the principle of utilize clockwise, the relevant error of gyroscope constant value sum of errors acceleration being cancelled out each other when being rotated counterclockwise, the constant multiplier and the alignment error of calculating gyro;

(4) utilize three-axle table that LIMU is carried out symmetrical 24 position static demarcating tests; The rotation three-axle table makes three coordinate axis of X, Y, Z of LIMU overlap with local geographic coordinate system; Rotate three-axle table then successively; X, the Y of LIMU, the sensing of three coordinate axis of Z are changed, rotate and to obtain 24 diverse locations 24 times, on each position, write down the output data of 3～5 minutes LIMU;

(5) based on each output data and rotational-angular velocity of the earth of LIMU on each position and acceleration of gravity in the relation between the projection components on each; On the basis of LIMU error mathematic model; Adopt symmetric position error phase elimination, the relevant error term of constant value drift, acceleration and accelerometer constant multiplier, the accelerometer that calculate laser gyro often are worth biasing, accelerometer alignment error;

(6) the rotation three-axle table makes three coordinate axis of X, Y, X of LIMU overlap with local geographic coordinate system, sets high and low temperature cyclic test parameter, comprises maximum temperature T _HBe 45 ℃～55 ℃, minimum temperature T _LBe-40 ℃～-30 ℃, temperature retention time t _TBe 150～180 minutes, rate temperature change v _TBe 1～3 ℃/minute, the temperature that incubator is set changes according to following rule: 1. at T _MInsulation t _T2. with-v _TSpeed from T _MBe cooled to T _L3. at T _LInsulation t _T4. with v _TSpeed from T _LBe warming up to T _H5. at T _HInsulation t _T6. with-v _TSpeed from T _HBe cooled to T _M7. at T _MInsulation t _TRecord LIMU output data is noted the temperature data that laser gyro and accelerometer are exported simultaneously;

(7), calculate in the temperature cycling test process and T according to the output data of LIMU record _MThe departure that laser gyro constant value drift and accelerometer often are worth biasing and are produced under the isoperibol; Bring in the temperature error model that laser gyro constant value drift and accelerometer often be worth biasing; Carry out linear fit with the temperature data of laser gyro and accelerometer output, calculate a temperature coefficient q of X, Y, three direction laser gyros of Z constant value drift _I1And q _I2(i=x, y, z), secondary temperature coefficient q _I3And q _I4, thermograde coefficient q _I5, temperature variation rate coefficient q _I6And q _I7, three directional acceleration meters often are worth a temperature coefficient e of biasing _I1, secondary temperature coefficient e _I2With temperature variation rate coefficient e _I3Totally 30 coefficients;

Described temperature error model comprises that laser gyro constant value drift temperature error model and accelerometer often are worth the bias temperature error model, respectively as follows:

$D_i^m=D_{i0}+q_{i1}{T}_{i1}^m+q_{i2}{T}_{i2}^m+q_{i3}{\left(T_{i1}^m\right)}^2+q_{i4}{\left(T_{i2}^m\right)}^2+q_{i5}(T_{i1}^m-T_{i2}^m)+q_{i6}(T_{i1}^m-T_{i1}^{m-1})+q_{i7}(T_{i2}^m-T_{i2}^{m-1})$

$S_i^m=S_{i0}+e_{i1}{T}_i^m+e_{i2}{\left(T_i^m\right)}^2+e_{i3}(T_i^m-T_i^{m-1})$

Wherein,

(z) the direction laser gyro is inclined to one side in m normal value constantly zero, D for i=x, y for i _I0For the laser gyro of i direction at T _MNormal value during temperature zero is inclined to one side,

With

For the laser gyro of i direction in m the 1 road and the 2 tunnel temperature output valve constantly,

With

For the laser gyro of i direction in m-1 the 1 road and the 2 tunnel temperature output valve constantly, For i directional acceleration meter is setovered S in m normal value constantly _I0For i directional acceleration meter at T _MNormal value biasing during temperature,

With

Be respectively i directional acceleration meter in the m moment and m-1 temperature output valve constantly.

Principle of the present invention is: adopt system's inherent error is separated the strategy of demarcating with temperature error; Measure through long-term insulation under certain temperature spot makes LIMU reach the overall thermal equilibrium state; On this basis; The LIMU scaling method that combines through dynamic rotation and static 24 positions accurately obtain gyro constant multiplier, gyroscope constant value zero partially, add the meter constant multiplier, add system's inherent error coefficient such as the normal value biasing of meter, thereby eliminated high and low temperature change to gyroscope constant value zero partially with add the meter value influence of setovering and causing often; Be the basis with the system's inherent error coefficient under this isoperibol again; LIMU is carried out high and low temperature cycle labeling test; Continuous variation through environment temperature; Motivate gyroscope constant value among the LIMU zero partially and accelerometer often be worth the dynamic temperature error of biasing; Carry out linear fit with the temperature data of gyro and accelerometer output, calibrate a temperature coefficient, secondary temperature coefficient, thermograde coefficient and the temperature variation rate coefficient of gyroscope constant value drift, accelerometer often is worth biasing temperature coefficient, secondary temperature coefficient and a temperature variation rate coefficient; This method is separated system's inherent error under the constant temperature with the error that is caused by temperature variation; Improved the stated accuracy of LIMU system inherent error under the isoperibol; Motivate the system temperature error through the environment temperature dynamic change simultaneously; More real simulated the environment for use of LIMU in actual engineering, improved the service precision of LIMU under varying temperature environment greatly.

The present invention's advantage compared with prior art is: the measure of the present invention through LIMU was incubated in the three-axle table incubator midium or long term; System's inherent error is separated demarcation with temperature error; Improved the stated accuracy of LIMU system inherent error under the isoperibol; Dynamic change through environment temperature simultaneously motivates the system temperature error, is benchmark with the inherent error coefficient under the isoperibol, calibrates the temperature error coefficient that the inclined to one side and accelerometer of the normal value of laser gyro among the LIMU zero often is worth biasing; The employed error model of this method meets the environment for use of LIMU in actual engineering more, thereby has improved the service precision of LIMU under varying temperature environment greatly.

Description of drawings

Fig. 1 is the process flow diagram of laser Inertial Measurement Unit temperature calibration method of the present invention.

Fig. 2 is a dynamic rotation rating test method synoptic diagram of the present invention.

Fig. 3 is symmetrical 24 position static demarcating test method synoptic diagram of the present invention.

Fig. 4 is an incubator temperature variation curve synoptic diagram of the present invention.

Embodiment

The present invention adopts system's inherent error is separated the strategy of demarcating with temperature error; Measure through long-term insulation under certain temperature spot makes LIMU reach the overall thermal balance; The scaling method that adopts dynamically rotation and static 24 positions to combine accurately calibrates gyro constant multiplier under this temperature spot, gyroscope constant value drift, accelerometer constant multiplier and accelerometer and often is worth system's inherent error coefficients such as biasing; Utilize the inherent error coefficient of LIMU under this temperature spot again; LIMU is carried out high and low temperature cyclic test; Further calibrate gyroscope constant value drift, accelerometer and often be worth the temperature error coefficient of biasing, comprise temperature coefficient, secondary temperature coefficient, thermograde coefficient and a temperature variation rate coefficient totally 30 temperature correlation coefficients.

As shown in Figure 1, practical implementation step of the present invention is following:

1, the laser gyroscope inertia measurement unit is installed on the three-axle table that has incubator, setting the interior temperature of incubator is T _MBe 20 ℃～30 ℃, insulation is 6～8 hours under LIMU works on power state;

2, utilize turntable that LIMU is dynamically rotated rating test, rotating table overlaps X axle, Y axle, the Z axle of LIMU successively with the Z axle of turntable, and as shown in Figure 2, all the other diaxons are in the surface level, make turntable with angular speed ω in each position ₀Respectively rotate 360 ° around clockwise, the counterclockwise both direction of the Z of geographic coordinate system axle, record LIMU output data;

At first set up LIMU gyroscope error model equation suc as formula shown in (1),

$\left[\begin{array}{c}{N}_x/K_x\\ N_y/K_y\\ N_z/K_z\end{array}\right]=\left[\begin{array}{c}{D}_{x0}\\ D_{y0}\\ D_{z0}\end{array}\right]+\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}{A}_x\\ A_y\\ A_z\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ω}}_x\\ {\mathrm{\ω}}_y\\ {\mathrm{\ω}}_z\end{array}\right]---\left(1\right)$

Wherein, N _x, N _y, N _zBe respectively the angle increment (umber of pulse) that x in the test, y, three direction gyros of z are gathered, K _x, K _y, K _zBe respectively the constant multiplier of three direction gyros, D _X0, D _Y0, D _Z0The normal value zero that is respectively three direction gyros is inclined to one side, D _Ij(y z) is the relevant error coefficient of acceleration, A for i, j=x _x, A _y, A _zBe respectively the specific force of x, y, three direction inputs of z, M _Ij(y z) is the gyro misalignment coefficient, ω for i, j=x _x, ω _y, ω _zBe respectively x, y, three direction input angular velocities of z.

Rotating table overlaps the X axle of LIMU with the Z axle of three-axle table, Y axle and Z axle are in the surface level, make turntable with angular speed ω ₀The Z axle of platform of rotating turns clockwise 360 °, shown in Fig. 2 (a), is rotated counterclockwise 360 ° again, and shown in Fig. 2 (b), the output that obtains three direction gyros is suc as formula shown in (2)～(3),

$\left[\begin{array}{c}(N_{x+}^1/K_x)-D_{x0}\\ (N_{y+}^1/K_y)-D_{y0}\\ (N_{z+}^1/K_z)-D_{z0}\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}g\\ 0\\ 0\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ω}}_0+{\mathrm{\ω}}_U^t\\ {\mathrm{\ω}}_N^t\·\cos \left({\mathrm{\ω}}_{0}t\right)\\ {\mathrm{\ω}}_N^t\·\sin \left({\mathrm{\ω}}_{0}t\right)\end{array}\right]---\left(2\right)$

$\left[\begin{array}{c}(N_{x-}^1/K_x)-D_{x0}\\ (N_{y-}^1/K_y)-D_{y0}\\ (N_{z-}^1/K_z)-D_{z0}\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}g\\ 0\\ 0\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}-{\mathrm{\ω}}_0+{\mathrm{\ω}}_U^t\\ {\mathrm{\ω}}_N^t\·\cos \left({\mathrm{\ω}}_{0}t\right)\\ {-\mathrm{\ω}}_N^t\·\sin \left({\mathrm{\ω}}_{0}t\right)\end{array}\right]---\left(3\right)$

Wherein, Three pulses that the direction gyro is gathered when

expression is rotated counterclockwise; Three pulses that the direction gyro is gathered when

expression turns clockwise; G representes acceleration of gravity;

is the Z axle component of rotational-angular velocity of the earth under local Department of Geography,

be that the Y of rotational-angular velocity of the earth under local Department of Geography is to component.

In like manner, rotating table overlaps Y axle and the Z axle of LIMU successively with the Z axle of turntable, repeats above work, shown in Fig. 2 (c)～2 (f), notes the data of LIMU output.

3, utilize the LIMU output data that is write down, according to the LIMU error mathematic model, the principle of utilize clockwise, the relevant error of gyroscope constant value sum of errors acceleration being cancelled out each other when being rotated counterclockwise, the constant multiplier and the alignment error of calculating gyro;

The X axle of LIMU is overlapped under the situation 0～360 ° of gyro output data suitable, that be rotated counterclockwise carry out integration with the Z axle of three-axle table, establish C=2 π/ω simultaneously ₀Obtain (4)～(5) formula,

$\left[\begin{array}{c}({\∫}_0^C{N}_{x+}^1\mathrm{dt}/K_x)-D_{x0}\·C\\ ({\∫}_0^C{N}_{y+}^1\mathrm{dt}/K_y)-D_{y0}\·C\\ ({\∫}_0^C{N}_{z+}^1\mathrm{dt}/K_z)-D_{z0}\·C\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}g\·C\\ 0\\ 0\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}2\mathrm{\π}+{\mathrm{\ω}}_U^t\·C\\ 0\\ 0\end{array}\right]---\left(4\right)$

$\left[\begin{array}{c}({\∫}_0^C{N}_{x-}^1\mathrm{dt}/K_x)-D_{x0}\·C\\ ({\∫}_0^C{N}_{y-}^1\mathrm{dt}/K_y)-D_{y0}\·C\\ ({\∫}_0^C{N}_{z-}^1\mathrm{dt}/K_z)-D_{z0}\·C\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}g\·C\\ 0\\ 0\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}-2\mathrm{\π}+{\mathrm{\ω}}_U^t\·C\\ 0\\ 0\end{array}\right]---\left(5\right)$

(4) are deducted (5), obtain

$\left[\begin{array}{c}({\∫}_0^C{N}_{x+}^1\mathrm{dt}-{\∫}_0^C{N}_{x-}^1\mathrm{dt})/4\mathrm{\π}\\ ({\∫}_0^C{N}_{y+}^1\mathrm{dt}-{\∫}_0^C{N}_{y-}^1\mathrm{dt})/4\mathrm{\π}\\ ({\∫}_0^C{N}_{z+}^1\mathrm{dt}-{\∫}_0^C{N}_{z-}^1\mathrm{dt})/4\mathrm{\π}\end{array}\right]=\left[\begin{array}{c}{K}_x{M}_{\mathrm{xx}}\\ K_y{M}_{\mathrm{xy}}\\ K_z{M}_{\mathrm{xz}}\end{array}\right]---\left(6\right)$

In like manner, overlap with the Z axle of three-axle table and carry out situation suitable, that be rotated counterclockwise, obtain (7)～(8) formula for the Y axle of LIMU and Z axle,

$\left[\begin{array}{c}({\∫}_0^C{N}_{x+}^2\mathrm{dt}-{\∫}_0^C{N}_{x-}^2\mathrm{dt})/4\mathrm{\π}\\ ({\∫}_0^C{N}_{y+}^2\mathrm{dt}-{\∫}_0^C{N}_{y-}^2\mathrm{dt})/4\mathrm{\π}\\ ({\∫}_0^C{N}_{z+}^2\mathrm{dt}-{\∫}_0^C{N}_{z-}^2\mathrm{dt})/4\mathrm{\π}\end{array}\right]=\left[\begin{array}{c}{K}_x{M}_{\mathrm{yx}}\\ K_y{M}_{\mathrm{yy}}\\ K_z{M}_{\mathrm{yz}}\end{array}\right]---\left(7\right)$

$\left[\begin{array}{c}({\∫}_0^C{N}_{x+}^3\mathrm{dt}-{\∫}_0^C{N}_{x-}^3\mathrm{dt})/4\mathrm{\π}\\ ({\∫}_0^C{N}_{y+}^3\mathrm{dt}-{\∫}_0^C{N}_{y-}^3\mathrm{dt})/4\mathrm{\π}\\ ({\∫}_0^C{N}_{z+}^3\mathrm{dt}-{\∫}_0^C{N}_{z-}^3\mathrm{dt})/4\mathrm{\π}\end{array}\right]=\left[\begin{array}{c}{K}_x{M}_{\mathrm{zx}}\\ K_y{M}_{\mathrm{zy}}\\ K_z{M}_{\mathrm{zz}}\end{array}\right]---\left(8\right)$

According to the relation between (6)～(8), the constant multiplier that can obtain gyro is:

$K_x=\frac{1}{4\mathrm{\π}}\sqrt{{({\∫}_0^C{N}_{x+}^1\mathrm{dt}-{\∫}_0^C{N}_{x-}^1\mathrm{dt})}^2+{({\∫}_0^C{N}_{x+}^2\mathrm{dt}-{\∫}_0^C{N}_{x-}^2\mathrm{dt})}^2+{({\∫}_0^C{N}_{x+}^3\mathrm{dt}-{\∫}_0^C{N}_{x-}^3\mathrm{dt})}^2}---\left(9\right)$

$K_y=\frac{1}{4\mathrm{\π}}\sqrt{{({\∫}_0^C{N}_{y+}^1\mathrm{dt}-{\∫}_0^C{N}_{y-}^1\mathrm{dt})}^2+{({\∫}_0^C{N}_{y+}^2\mathrm{dt}-{\∫}_0^C{N}_{y-}^2\mathrm{dt})}^2+{({\∫}_0^C{N}_{y+}^3\mathrm{dt}-{\∫}_0^C{N}_{y-}^3\mathrm{dt})}^2}---\left(10\right)$

$K_z=\frac{1}{4\mathrm{\π}}\sqrt{{({\∫}_0^C{N}_{z+}^1\mathrm{dt}-{\∫}_0^C{N}_{z-}^1\mathrm{dt})}^2+{({\∫}_0^C{N}_{z+}^2\mathrm{dt}-{\∫}_0^C{N}_{z-}^2\mathrm{dt})}^2+{({\∫}_0^C{N}_{z+}^3\mathrm{dt}-{\∫}_0^C{N}_{z-}^3\mathrm{dt})}^2}---\left(11\right)$

The alignment error that simultaneously, can obtain gyro is:

$\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]=\left[\begin{array}{ccc}\frac{{\∫}_0^C{N}_{x+}^1\mathrm{dt}-{\∫}_0^C{N}_{x-}^1\mathrm{dt}}{4\mathrm{\π}{K}_x}& \frac{{\∫}_0^C{N}_{x+}^2\mathrm{dt}-{\∫}_0^C{N}_{x-}^2\mathrm{dt}}{4\mathrm{\π}{K}_x}& \frac{{\∫}_0^C{N}_{x+}^3\mathrm{dt}-{\∫}_0^C{N}_{x-}^3\mathrm{dt}}{4\mathrm{\π}{K}_x}\\ \frac{{\∫}_0^C{N}_{y+}^1\mathrm{dt}-{\∫}_0^C{N}_{y-}^1\mathrm{dt}}{4\mathrm{\π}{K}_y}& \frac{{\∫}_0^C{N}_{y+}^2\mathrm{dt}-{\∫}_0^C{N}_{y-}^2\mathrm{dt}}{4\mathrm{\π}{K}_y}& \frac{{\∫}_0^C{N}_{y+}^3\mathrm{dt}-{\∫}_0^C{N}_{y-}^3\mathrm{dt}}{4\mathrm{\π}{K}_y}\\ \frac{{\∫}_0^C{N}_{z+}^1\mathrm{dt}-{\∫}_0^C{N}_{z-}^1\mathrm{dt}}{4\mathrm{\π}{K}_z}& \frac{{\∫}_0^C{N}_{z+}^2\mathrm{dt}-{\∫}_0^C{N}_{z-}^2\mathrm{dt}}{4\mathrm{\π}{K}_z}& \frac{{\∫}_0^C{N}_{z+}^3\mathrm{dt}-{\∫}_0^C{N}_{z-}^3\mathrm{dt}}{4\mathrm{\π}{K}_z}\end{array}\right]---\left(12\right)$

4, utilize three-axle table that LIMU is carried out symmetrical 24 position static demarcating tests; The rotation three-axle table makes three coordinate axis of XYZ of LIMU overlap with local geographic coordinate system; Revolving-turret successively then; The sensing of three coordinate axis of XYZ of LIMU is changed, rotate and to obtain 24 diverse locations 24 times, on each position, write down the output data of 3～5 minutes LIMU; Concrete 24 positions are as shown in Figure 3, and concrete steps are following:

(1) the adjustment three-axle table makes the sky of x axle and local geographic coordinate system of LIMU overlap in the same way to axle, and the Y of LIMU, Z axle point to the east orientation and the north orientation of Department of Geography respectively, shown in Fig. 3 (1), and in this position, i.e. the 1st location records 3～5-minute data;

(2) be rotated counterclockwise the three-axle table outside framework, rotate 90 ° at every turn, the record 5-minute data to another position; Rotation is 4 positions altogether, comprise the 1st position, shown in Fig. 3 (1)～Fig. 3 (4); Each position is write down 3～5-minute data respectively, has write down 1～4 position data altogether;

(3) the adjustment three-axle table makes the sky of X axle and local geographic coordinate system of LIMU oppositely overlap to axle, and the Y of LIMU, Z axle point to the east orientation and the south orientation of Department of Geography respectively, shown in Fig. 3 (5), and in this position, i.e. the 5th location records 3～5-minute data;

(4) be rotated counterclockwise the three-axle table outside framework, rotate 90 ° at every turn, the record 5-minute data to another position; Rotation is 4 positions altogether, comprise the 5th position, shown in Fig. 3 (5)～Fig. 3 (8); Each position is write down 3～5-minute data respectively, has write down 5～8 position datas altogether;

(5) the adjustment three-axle table makes the sky of y axle and local geographic coordinate system of LIMU overlap in the same way to axle, and the X of LIMU, Z axle point to the north orientation and the east orientation of Department of Geography respectively, shown in Fig. 3 (9), and in this position, i.e. the 9th location records 3～5-minute data;

(6) be rotated counterclockwise the three-axle table outside framework, rotate 90 ° at every turn, the record 5-minute data to another position; Rotation is 4 positions altogether, comprise the 9th position, shown in Fig. 3 (9)～Fig. 3 (12); Each position is write down 3～5-minute data respectively, has write down 9～12 position datas altogether;

(7) the adjustment three-axle table makes the sky of Y axle and local geographic coordinate system of LIMU oppositely overlap to axle, and the X of LIMU, Z axle point to the south orientation and the east orientation of Department of Geography respectively, shown in Fig. 3 (13), and in this position, i.e. the 13rd location records 3～5-minute data;

(8) be rotated counterclockwise the three-axle table outside framework, rotate 90 ° at every turn, the record 5-minute data to another position; Rotation is 4 positions altogether, comprise the 13rd position, shown in Fig. 3 (13)～Fig. 3 (16); Each position is write down 3～5-minute data respectively, has write down 13～16 position datas altogether;

(9) the adjustment three-axle table makes the sky of Z axle and local geographic coordinate system of LIMU overlap in the same way to axle, and the X of LIMU, Y axle point to the east orientation and the north orientation of Department of Geography respectively, shown in Fig. 3 (17), and in this position, i.e. the 17th location records 3～5-minute data;

(10) be rotated counterclockwise the three-axle table outside framework, rotate 90 ° at every turn, the record 5-minute data to another position; Rotation is 4 positions altogether, comprise the 17th position, shown in Fig. 3 (17)～Fig. 3 (20); Each position is write down 3～5-minute data respectively, has write down 17～20 position datas altogether;

(11) the adjustment three-axle table makes the sky of Z axle and local geographic coordinate system of LIMU oppositely overlap to axle, and the X of LIMU, Y axle point to the east orientation and the south orientation of Department of Geography respectively, shown in Fig. 3 (21), and in this position, i.e. the 21st location records 3～5-minute data;

(12) be rotated counterclockwise the turntable outside framework, rotate 90 ° at every turn, the record 5-minute data to another position; Rotation is 4 positions altogether, comprise the 21st position, shown in Fig. 3 (21)～Fig. 3 (24); Each position is write down 3～5-minute data respectively, has write down 21～24 position datas altogether.

5, based on each output data and rotational-angular velocity of the earth of LIMU on each position and acceleration of gravity in the relation between the projection components on each; On the basis of LIMU error mathematic model; Adopt symmetric position error phase elimination, the relevant error term of constant value drift, acceleration and accelerometer constant multiplier, the accelerometer that calculate laser gyro often are worth biasing, accelerometer alignment error;

Under 1～4 situation of position, the output of gyro is suc as formula shown in (13)～(16),

$\left[\begin{array}{c}(F_x^1/K_x)-D_{x0}\\ (F_y^1/K_y)-D_{y0}\\ (F_z^1/K_z)-D_{z0}\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}g\\ 0\\ 0\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ω}}_U^t\\ 0\\ {\mathrm{\ω}}_N^t\end{array}\right]---\left(13\right)$

$\left[\begin{array}{c}(F_x^2/K_x)-D_{x0}\\ (F_y^2/K_y)-D_{y0}\\ (F_z^2/K_z)-D_{z0}\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}g\\ 0\\ 0\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ω}}_U^t\\ {\mathrm{\ω}}_N^t\\ 0\end{array}\right]---\left(14\right)$

$\left[\begin{array}{c}(F_x^3/K_x)-D_{x0}\\ (F_y^3/K_y)-D_{y0}\\ (F_z^3/K_z)-D_{z0}\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}g\\ 0\\ 0\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ω}}_U^t\\ 0\\ {-\mathrm{\ω}}_N^t\end{array}\right]---\left(15\right)$

$\left[\begin{array}{c}(F_x^4/K_x)-D_{x0}\\ (F_y^4/K_y)-D_{y0}\\ (F_z^4/K_z)-D_{z0}\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}g\\ 0\\ 0\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ω}}_U^t\\ {-\mathrm{\ω}}_N^t\\ 0\end{array}\right]---\left(16\right)$

Wherein,

is illustrated in the output of i direction gyro under the m position; (13)～(16) formula addition is obtained (17) formula,

$\left[\begin{array}{c}\left(F_x^{10}\right)/K_x-D_{x0}\\ \left(F_y^{10}\right)/K_y-D_{y0}\\ \left(F_z^{10}\right)/K_z-D_{z0}\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}g\\ 0\\ 0\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ω}}_U^t\\ 0\\ 0\end{array}\right]---\left(17\right)$

Wherein, Adding up of expression i direction gyro output data; In like manner; After the output addition for 5～8 position gyroes; Obtain (18) formula, wherein,

$\left[\begin{array}{c}\left(F_x^{20}\right)/K_x-D_{x0}\\ \left(F_y^{20}\right)/K_y-D_{y0}\\ \left(F_z^{20}\right)/K_z-D_{z0}\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}-g\\ 0\\ 0\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}{-\mathrm{\ω}}_U^t\\ 0\\ 0\end{array}\right]---\left(18\right)$

For 1～8 position, be the x axle that satisfies LIMU with the sky of geographic coordinate system to 8 positions of symmetry that axle overlaps, in like manner; For 9～16 positions; Be the Y axle that satisfies LIMU with the sky of geographic coordinate system to 8 positions of symmetry that axle overlaps, can obtain (19)～(20) two formulas, wherein $F_i^{30}=(F_i^9+F_i^{10}+F_i^{11}+F_i^{12})/4,$ $F_i^{40}=(F_i^{13}+F_i^{14}+F_i^{15}+F_i^{16})/4,$

$\left[\begin{array}{c}\left(F_x^{30}\right)/K_x-D_{x0}\\ \left(F_y^{30}\right)/K_y-D_{y0}\\ \left(F_z^{30}\right)/K_z-D_{z0}\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}0\\ g\\ 0\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}0\\ {\mathrm{\ω}}_U^t\\ 0\end{array}\right]---\left(19\right)$

$\left[\begin{array}{c}\left(F_x^{40}\right)/K_x-D_{x0}\\ \left(F_y^{40}\right)/K_y-D_{y0}\\ \left(F_z^{40}\right)/K_z-D_{z0}\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}0\\ -g\\ 0\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}0\\ {-\mathrm{\ω}}_U^t\\ 0\end{array}\right]---\left(20\right)$

For 17～24 positions, be the Z axle that satisfies LIMU with the sky of geographic coordinate system to 8 positions of symmetry that axle overlaps, can obtain (21)～(22) two formulas, $F_i^{50}=(F_i^{17}+F_i^{18}+F_i^{19}+F_i^{20})/4,$ $F_i^{60}=(F_i^{21}+F_i^{22}+F_i^{23}+F_i^{24})/4,$

$\left[\begin{array}{c}\left(F_x^{50}\right)/K_x-D_{x0}\\ \left(F_y^{50}\right)/K_y-D_{y0}\\ \left(F_z^{50}\right)/K_z-D_{z0}\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}0\\ 0\\ g\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}0\\ 0\\ {\mathrm{\ω}}_U^t\end{array}\right]---\left(21\right)$

$\left[\begin{array}{c}\left(F_x^{60}\right)/K_x-D_{x0}\\ \left(F_y^{60}\right)/K_y-D_{y0}\\ \left(F_z^{60}\right)/K_z-D_{z0}\end{array}\right]=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{yx}}& D_{\mathrm{zx}}\\ D_{\mathrm{xy}}& D_{\mathrm{yy}}& D_{\mathrm{zy}}\\ D_{\mathrm{xz}}& D_{\mathrm{yz}}& D_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}0\\ 0\\ -g\end{array}\right]+\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}0\\ 0\\ {-\mathrm{\ω}}_U^t\end{array}\right]---\left(22\right)$

Through (17)～(22) formula, bring gyro constant multiplier and the alignment error obtained into, can calculate the normal value zero inclined to one side D of gyro _I0With relevant with g coefficient D _Ij(i, j=x, y, z), D _IjCoefficient between expression i direction gyro and the input of j directional acceleration, specifically suc as formula shown in (23)～(24),

$\left[\begin{array}{c}{D}_{x0}\\ D_{y0}\\ D_{z0}\end{array}\right]=\frac{1}{6}\left[\begin{array}{ccc}1/K_x& 0& 0\\ 0& 1/K_y& 0\\ 0& 0& 1/K_z\end{array}\right]\left[\begin{array}{c}{F}_x^{10}+F_x^{20}+F_x^{30}+F_x^{40}+F_x^{50}+F_x^{60}\\ F_y^{10}+F_y^{20}+F_y^{30}+F_y^{40}+F_y^{50}+F_y^{60}\\ F_z^{10}+F_z^{20}+F_z^{30}+F_z^{40}+F_z^{50}+F_z^{60}\end{array}\right]---\left(23\right)$

$\left[\begin{array}{ccc}{D}_{x0}& D_{y0}& D_{z0}\\ M_{\mathrm{xx}}& M_{\mathrm{yx}}& M_{\mathrm{zx}}\\ M_{\mathrm{xy}}& M_{\mathrm{yy}}& M_{\mathrm{zy}}\\ M_{\mathrm{xz}}& M_{\mathrm{yz}}& M_{\mathrm{zz}}\end{array}\right]={\left\{\left[\begin{array}{cccc}1& g& 0& 0\\ 1& -g& 0& 0\\ 1& 0& g& 0\\ 1& 0& -g& 0\\ 1& 0& 0& g\\ 1& 0& 0& -g\end{array}\right]\right\}}^{+}\left[\begin{array}{ccc}{F}_x^{10}/K_x& F_y^{10}/K_y& F_y^{10}/K_y\\ F_x^{20}/K_x& F_y^{20}/K_y& F_y^{20}/K_y\\ F_x^{30}/K_x& F_y^{30}/K_y& F_y^{30}/K_y\\ F_x^{40}/K_x& F_y^{40}/K_y& F_y^{40}/K_y\\ F_x^{50}/K_x& F_y^{50}/K_y& F_y^{50}/K_y\\ F_x^{60}/K_x& F_y^{60}/K_y& F_y^{60}/K_y\end{array}\right]---\left(24\right)$

Wherein, the generalized inverse of matrix is asked in "+" in upper right corner expression; So far, obtain all relevant error coefficients of gyro among the LIMU, comprised gyro constant multiplier, gyroscope constant value drift, gyro misalignment coefficient, the relevant error coefficient of acceleration.

Set up LIMU accelerometer error model equation suc as formula shown in (25),

$\left[\begin{array}{c}{X}_x\\ X_y\\ X_z\end{array}\right]=\left[\begin{array}{cccc}{S}_{x0}& S_x{L}_{\mathrm{xx}}& S_x{L}_{\mathrm{yx}}& S_x{L}_{\mathrm{zx}}\\ S_{y0}& S_y{L}_{\mathrm{xy}}& S_y{L}_{\mathrm{yy}}& S_y{L}_{\mathrm{zy}}\\ S_{z0}& S_z{L}_{\mathrm{xz}}& S_z{L}_{\mathrm{yz}}& S_z{L}_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}1\\ A_x\\ A_y\\ A_z\end{array}\right]---\left(25\right)$

Wherein, X _x, X _y, X _zBe respectively the specific force (pulsed quantity) that x in the test, y, three directional acceleration meters of z are gathered, S _x, S _y, S _zBe respectively the constant multiplier of three directional acceleration meters, S _X0, S _Y0, S _Z0Be respectively the normal value biasing of three directional acceleration meters, L _Ij(y z) is accelerometer alignment error coefficient, A for i, j=x _x, A _y, A _zBe respectively the specific force of x, y, three direction inputs of z.The output of the accelerometer of position 1～4 is added up, obtains formula (26),

$\left[\begin{array}{c}{X}_x^1\\ X_y^1\\ X_z^1\end{array}\right]=\left[\begin{array}{cccc}{S}_{x0}& S_x{L}_{\mathrm{xx}}& S_x{L}_{\mathrm{yx}}& S_x{L}_{\mathrm{zx}}\\ S_{y0}& S_y{L}_{\mathrm{xy}}& S_y{L}_{\mathrm{yy}}& S_y{L}_{\mathrm{zy}}\\ S_{z0}& S_z{L}_{\mathrm{xz}}& S_z{L}_{\mathrm{yz}}& S_z{L}_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}1\\ g\\ 0\\ 0\end{array}\right]---\left(26\right)$

Wherein,

expression i directional acceleration meter adds up the back divided by 4 averages that obtain in 1～4 position output data; In like manner, for 5～24 positions, can obtain (27)～(31) formula,

$\left[\begin{array}{c}{X}_x^2\\ X_y^2\\ X_z^2\end{array}\right]=\left[\begin{array}{cccc}{S}_{x0}& S_x{L}_{\mathrm{xx}}& S_x{L}_{\mathrm{yx}}& S_x{L}_{\mathrm{zx}}\\ S_{y0}& S_y{L}_{\mathrm{xy}}& S_y{L}_{\mathrm{yy}}& S_y{L}_{\mathrm{zy}}\\ S_{z0}& S_z{L}_{\mathrm{xz}}& S_z{L}_{\mathrm{yz}}& S_z{L}_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}1\\ -g\\ 0\\ 0\end{array}\right]---\left(27\right)$

$\left[\begin{array}{c}{X}_x^3\\ X_y^3\\ X_z^3\end{array}\right]=\left[\begin{array}{cccc}{S}_{x0}& S_x{L}_{\mathrm{xx}}& S_x{L}_{\mathrm{yx}}& S_x{L}_{\mathrm{zx}}\\ S_{y0}& S_y{L}_{\mathrm{xy}}& S_y{L}_{\mathrm{yy}}& S_y{L}_{\mathrm{zy}}\\ S_{z0}& S_z{L}_{\mathrm{xz}}& S_z{L}_{\mathrm{yz}}& S_z{L}_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}1\\ 0\\ g\\ 0\end{array}\right]---\left(28\right)$

$\left[\begin{array}{c}{X}_x^4\\ X_y^4\\ X_z^4\end{array}\right]=\left[\begin{array}{cccc}{S}_{x0}& S_x{L}_{\mathrm{xx}}& S_x{L}_{\mathrm{yx}}& S_x{L}_{\mathrm{zx}}\\ S_{y0}& S_y{L}_{\mathrm{xy}}& S_y{L}_{\mathrm{yy}}& S_y{L}_{\mathrm{zy}}\\ S_{z0}& S_z{L}_{\mathrm{xz}}& S_z{L}_{\mathrm{yz}}& S_z{L}_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}1\\ 0\\ -g\\ 0\end{array}\right]---\left(29\right)$

$\left[\begin{array}{c}{X}_x^5\\ X_y^5\\ X_z^5\end{array}\right]=\left[\begin{array}{cccc}{S}_{x0}& S_x{L}_{\mathrm{xx}}& S_x{L}_{\mathrm{yx}}& S_x{L}_{\mathrm{zx}}\\ S_{y0}& S_y{L}_{\mathrm{xy}}& S_y{L}_{\mathrm{yy}}& S_y{L}_{\mathrm{zy}}\\ S_{z0}& S_z{L}_{\mathrm{xz}}& S_z{L}_{\mathrm{yz}}& S_z{L}_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}1\\ 0\\ 0\\ g\end{array}\right]---\left(30\right)$

$\left[\begin{array}{c}{X}_x^6\\ X_y^6\\ X_z^6\end{array}\right]=\left[\begin{array}{cccc}{S}_{x0}& S_x{L}_{\mathrm{xx}}& S_x{L}_{\mathrm{yx}}& S_x{L}_{\mathrm{zx}}\\ S_{y0}& S_y{L}_{\mathrm{xy}}& S_y{L}_{\mathrm{yy}}& S_y{L}_{\mathrm{zy}}\\ S_{z0}& S_z{L}_{\mathrm{xz}}& S_z{L}_{\mathrm{yz}}& S_z{L}_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{c}1\\ 0\\ 0\\ -g\end{array}\right]---\left(31\right)$

Utilize (27)～(31) formula, can directly calculate all error coefficients of accelerometer, shown in the formula of (32)～(34),

$\left[\begin{array}{ccc}{S}_{x0}& S_{y0}& S_{z0}\\ S_x{L}_{\mathrm{xx}}& S_y{L}_{\mathrm{yx}}& S_z{L}_{\mathrm{zx}}\\ S_x{L}_{\mathrm{xy}}& S_y{L}_{\mathrm{yy}}& S_z{L}_{\mathrm{zy}}\\ S_x{L}_{\mathrm{xz}}& S_y{L}_{\mathrm{yz}}& S_z{L}_{\mathrm{zz}}\end{array}\right]={\left\{\left[\begin{array}{cccc}1& g& 0& 0\\ 1& -g& 0& 0\\ 1& 0& g& 0\\ 1& 0& -g& 0\\ 1& 0& 0& g\\ 1& 0& 0& -g\end{array}\right]\right\}}^{+}\left[\begin{array}{ccc}{X}_x^1& X_y^1& X_z^1\\ X_x^2& X_y^2& X_z^2\\ X_x^3& X_y^3& X_z^3\\ X_x^4& X_y^4& X_z^4\\ X_x^5& X_y^5& X_z^5\\ X_x^6& X_y^6& X_z^6\end{array}\right]---\left(32\right)$

$\left[\begin{array}{c}{S}_x\\ S_y\\ S_z\end{array}\right]=\left[\begin{array}{c}\sqrt{{\left(S_x{L}_{\mathrm{xx}}\right)}^2+{\left(S_x{L}_{\mathrm{xy}}\right)}^2+{\left(S_x{L}_{\mathrm{xz}}\right)}^2}\\ \sqrt{{\left(S_y{L}_{\mathrm{yx}}\right)}^2+{\left(S_y{L}_{\mathrm{yy}}\right)}^2+{\left(S_y{L}_{\mathrm{yz}}\right)}^2}\\ \sqrt{{\left(S_z{L}_{\mathrm{zx}}\right)}^2+{\left(S_z{L}_{\mathrm{zy}}\right)}^2+{\left(S_z{L}_{\mathrm{zz}}\right)}^2}\end{array}\right]---\left(33\right)$

$\left[\begin{array}{ccc}{L}_{\mathrm{xx}}& L_{\mathrm{yx}}& L_{\mathrm{zx}}\\ L_{\mathrm{xy}}& L_{\mathrm{yy}}& L_{\mathrm{zy}}\\ L_{\mathrm{xz}}& L_{\mathrm{yz}}& L_{\mathrm{zz}}\end{array}\right]=\left[\begin{array}{ccc}{S}_{\mathrm{xx}}& S_{\mathrm{yx}}& S_{\mathrm{zx}}\\ S_{\mathrm{xy}}& S_{\mathrm{yy}}& S_{\mathrm{zy}}\\ S_{\mathrm{xz}}& S_{\mathrm{yz}}& S_{\mathrm{zz}}\end{array}\right]\left[\begin{array}{ccc}1/S_x& 0& 0\\ 0& 1/S_y& 0\\ 0& 0& 1/S_z\end{array}\right]---\left(34\right)$

So far, calibrated all error coefficients of accelerometer among the LIMU, comprised that accelerometer constant multiplier, accelerometer often are worth biasing and accelerometer alignment error.

6, the rotation three-axle table makes three coordinate axis of XYZ of LIMU overlap with local geographic coordinate system, sets high and low temperature cyclic test parameter, comprises maximum temperature T _HBe 45 ℃～55 ℃, minimum temperature T _LBe-40 ℃～-30 ℃, temperature retention time t _TBe 150～180 minutes, rate temperature change v _TBe 1～3 ℃/minute, the temperature that incubator is set changes according to following rule: 1. at T _MInsulation t _T2. with-v _TSpeed from T _MBe cooled to T _L3. at T _LInsulation t _T4. with v _TSpeed from T _LBe warming up to T _H5. at T _HInsulation t _T6. with-v _TSpeed from T _HBe cooled to T _M7. at T _MInsulation t _TAs shown in Figure 4, record LIMU output data is noted the temperature data that laser gyro and accelerometer are exported simultaneously;

7,, calculate in the temperature cycling test process and T according to the output data of LIMU record _MThe departure that laser gyro constant value drift and accelerometer often are worth biasing and are produced under the isoperibol; Bring in the temperature error model that laser gyro constant value drift and accelerometer often be worth biasing; Carry out linear fit with the temperature data of laser gyro and accelerometer output; Calculate a temperature coefficient, secondary temperature coefficient, thermograde coefficient and the temperature variation rate coefficient of laser gyro constant value drift, a temperature coefficient, secondary temperature coefficient and the temperature variation rate coefficient that accelerometer often is worth biasing be totally 30 coefficients;

Described temperature error model comprises that laser gyro constant value drift temperature error model and accelerometer often are worth the bias temperature error model, respectively suc as formula shown in (35)～(36):

$D_i^m=D_{i0}+q_{i1}{T}_{i1}^m+q_{i2}{T}_{i2}^m+q_{i3}{\left(T_{i1}^m\right)}^2+q_{i4}{\left(T_{i2}^m\right)}^2+q_{i5}(T_{i1}^m-T_{i2}^m)+q_{i6}(T_{i1}^m-T_{i1}^{m-1})+q_{i7}(T_{i2}^m-T_{i2}^{m-1})---\left(35\right)$

$S_i^m=S_{i0}+e_{i1}{T}_i^m+e_{i2}{\left(T_i^m\right)}^2+e_{i3}(T_i^m-T_i^{m-1})---\left(36\right)$

Wherein,

(z) the direction laser gyro is inclined to one side in m normal value constantly zero, D for i=x, y for i _I0For the laser gyro of i direction at T _MThe time normal value zero partially,

With

For the laser gyro of i direction in m the 1 road and the 2 tunnel temperature output valve constantly,

With

For the laser gyro of i direction at m-1 the 1 road and the 2 tunnel temperature output valve constantly, q _I1～q _I7Be followed successively by a temperature coefficient, secondary temperature coefficient, thermograde coefficient and the temperature variation rate coefficient of the laser gyro of i direction,

For i directional acceleration meter is setovered S in m normal value constantly _I0For i directional acceleration meter at T _MThe time the biasing of normal value,

With

Be respectively i directional acceleration meter at the m moment and m-1 temperature output valve constantly, e _I1～e _I3Be followed successively by a temperature coefficient, secondary temperature coefficient and the thermograde coefficient of i directional acceleration meter.Formula (37) has been represented normal the value zero inclined to one side and T of gyro under the temperature variations _MThe relation of normal value under the constant temperature situation zero between partially, formula (38) has been represented the normal value biasing and the T of accelerometer under the temperature variations _MRelation between the normal value biasing under the constant temperature situation,

$D_i^m-D_{i0}=K_i(N_i^m-N_{i0})---\left(37\right)$

$S_i^m-S_{i0}=S_i(X_i^m-X_{i0})---\left(38\right)$

Wherein

Be the output that i direction gyro under the temperature variation environment is gathered at m constantly, N _I0Be T _MI direction gyro output under the isoperibol can be through the 1. stage T in the 6th step _MInsulation t _TThe gyro data of exporting in the process is asked on average and is obtained;

Be i directional acceleration meter under the temperature variation environment

At the output that m gathers constantly, N _I0Be T _MI directional acceleration meter output under the isoperibol can be through the 1. stage T in the 6th step _MInsulation t _TThe accelerometer data of exporting in the process is asked on average and is obtained; All temperatures coefficient of gyro and accelerometer can be obtained in through type (38)～(39),

$\left[\begin{array}{c}{q}_{i1}\\ q_{i2}\\ \·\\ \·\\ \·\\ q_{i7}\end{array}\right]{=\left[\begin{array}{ccccccc}{T}_{i1}^1& T_{i2}^1& {\left(T_{i1}^1\right)}^2& {\left(T_{i2}^1\right)}^2& T_{i1}^1-T_{i2}^1& T_{i1}^1-T_{i1}^0& T_{i2}^1-T_{i2}^0\\ T_{i1}^2& T_{i2}^2& {\left(T_{i1}^2\right)}^2& {\left(T_{i2}^2\right)}^2& T_{i1}^2-T_{i2}^2& T_{i1}^2-T_{i1}^1& T_{i2}^2-T_{i2}^1\\ \·& & & & & & \·\\ \·& & & \·\·\·& & & \·\\ \·& & & & & & \·\\ T_{i1}^P& T_{i2}^P& {\left(T_{i1}^P\right)}^2& {\left(T_{i2}^P\right)}^2& T_{i1}^P-T_{i2}^P& T_{i1}^P-T_{i1}^{P-1}& T_{i2}^P-T_{i2}^{P-1}\end{array}\right]}^{+}\left[\begin{array}{c}{D}_i^1-D_{i0}\\ D_i^2-D_{i0}\\ \·\\ \·\\ \·\\ D_i^P-D_{i0}\end{array}\right]---\left(38\right)$

$\left[\begin{array}{c}{e}_{i1}\\ e_{i2}\\ e_{i3}\end{array}\right]{=\left[\begin{array}{ccc}{T}_i^1& {\left(T_i^1\right)}^2& T_i^1-T_i^0\\ T_i^2& {\left(T_i^2\right)}^2& T_i^2-T_i^1\\ \·& \·& \·\\ \·& \·& \·\\ \·& \·& \·\\ T_i^P& {\left(T_i^P\right)}^2& T_i^P-T_i^{P-1}\end{array}\right]}^{+}\left[\begin{array}{c}{S}_i^1-S_{i0}\\ S_i^2-S_{i0}\\ \·\\ \·\\ \·\\ S_i^P-S_{i0}\end{array}\right]---\left(39\right)$

So far, calibrated a temperature coefficient q of X among the LIMU, Y, three direction laser gyros of Z constant value drift _I1And q _I2(i=x, y, z), secondary temperature coefficient q _I3And q _I4, thermograde coefficient q _I5, temperature variation rate coefficient q _I6And q _I7, three directional acceleration meters often are worth a temperature coefficient e of biasing _I1, secondary temperature coefficient e _I2With temperature variation rate coefficient e _I3Totally 30 coefficients are accomplished the temperature calibration of laser gyroscope inertia measurement unit.

The present invention does not set forth the known technology that part belongs to those skilled in the art in detail.

Claims (1)

1. the temperature calibration method of a laser gyroscope inertia measurement unit is characterized in that performing step is following:

(1) laser gyroscope inertia measurement unit (LIMU) is installed on the three-axle table that has incubator, setting the interior temperature of incubator is T _MBe 20 ℃～30 ℃, insulation is 6～8 hours under LIMU works on power state;

(2) utilize three-axle table that LIMU is dynamically rotated rating test, rotate three-axle table and successively X axle, Y axle, the Z axle of LIMU are overlapped with the Z axle of three-axle table, all the other diaxons are in the surface level, make three-axle table with angular speed ω in each position ₀Respectively rotate 360 ° around clockwise, the counterclockwise both direction of the Z of geographic coordinate system axle, record LIMU output data;

(3) utilize the LIMU output data that is write down, according to the LIMU error mathematic model, the principle of utilize clockwise, the relevant error of gyroscope constant value sum of errors acceleration being cancelled out each other when being rotated counterclockwise, the constant multiplier and the alignment error of calculating gyro;

(4) utilize three-axle table that LIMU is carried out symmetrical 24 position static demarcating tests; The rotation three-axle table makes three coordinate axis of X, Y, Z of LIMU overlap with local geographic coordinate system; Rotate three-axle table then successively; X, the Y of LIMU, the sensing of three coordinate axis of Z are changed, rotate and to obtain 24 diverse locations 24 times, on each position, write down the output data of 3～5 minutes LIMU;

(5) based on each output data and rotational-angular velocity of the earth of LIMU on each position and acceleration of gravity in the relation between the projection components on each; On the basis of LIMU error mathematic model; Adopt symmetric position error phase elimination, the relevant error term of constant value drift, acceleration and accelerometer constant multiplier, the accelerometer that calculate laser gyro often are worth biasing, accelerometer alignment error;

(6) revolving-turret makes three coordinate axis of xyz of LIMU overlap with local geographic coordinate system, sets high and low temperature cyclic test parameter, comprises maximum temperature T _HBe 45 ℃～55 ℃, minimum temperature T _LBe-40 ℃～-30 ℃, temperature retention time t _TBe 150～180 minutes, rate temperature change v _TBe 1～3 ℃/minute, the incubator temperature that three-axle table is set changes according to following rule: 1. at T _MInsulation t _T2. with-v _TSpeed from T _MBe cooled to T _L3. at T _LInsulation t _T4. with v _TSpeed from T _LBe warming up to T _H5. at T _HInsulation t _T6. with-v _TSpeed from T _HBe cooled to T _M7. at T _MInsulation t _TRecord LIMU output data is noted the temperature data that laser gyro and accelerometer are exported simultaneously;

(7), calculate in the temperature cycling test process and T according to the output data of LIMU record _MThe departure that laser gyro constant value drift and accelerometer often are worth biasing and are produced under the isoperibol; Bring in the temperature error model that laser gyro constant value drift and accelerometer often be worth biasing; Carry out linear fit with the temperature data of laser gyro and accelerometer output, calculate a temperature coefficient q of X, Y, three direction laser gyros of Z constant value drift _I1And q _I2, secondary temperature coefficient q _I3And q _I4, thermograde coefficient q _I5, temperature variation rate coefficient q _I6And q _I7, three directional acceleration meters often are worth a temperature coefficient e of biasing _I1, secondary temperature coefficient e _I2With temperature variation rate coefficient e _I3Totally 30 coefficients, i=x, y, z.

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