CN102393210B - 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

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

Background technology

Laser gyro, as the desirable device of inertial navigation, has the features such as start-up time is short, dynamic range is large, reliability is high, the life-span is long, digital output.In recent years, laser gyro strap down inertial navigation system successfully applies to multiple 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, environment temperature acute variation, directly affect the variation of LIMU inherent error coefficient, particularly gyroscope constant value zero partially and accelerometer bias, to vary with temperature generation big ups and downs, thereby affect the precision of laser gyro and accelerometer output data, further affect the operating accuracy of inertial navigation system.Therefore, laser gyro strap down inertial navigation must be tested and be determined gyroscope constant value in LIMU zero partially and the temperature error coefficient of accelerometer bias by temperature calibration before use, and compensates in system.

Traditional LIMU temperature calibration method is mainly that the constant temperature based on many temperature spots is demarcated, the scaling method that this scaling method adopts dynamic rotary 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 to linear fit, obtain corresponding temperature error coefficient.There are following two problems in the method: 1, system temperature error does not thoroughly separate with system inherent error, has phase mutual interference; 2, only demarcate the error under many groups steady temperature environment, do not demarcated the error under temperature dynamic changing environment.Therefore, use the method the LIMU system inherent error coefficient and the temperature error coefficient precision that calibrate limited, be not suitable for temperature fast, the engineering application scenario of acute variation.In practical engineering application environment, the beginning of working from power on of laser gyroscope inertia measurement unit, self temperature of gyro and accelerometer is all the time in change procedure, the impact of the ambient temperature being changed on the one hand, be subject on the one hand the impact of gyro and accelerometer self work heating, thereby make gyro and accelerometer self form from inside to outside complicated temperature field, have a strong impact on the measuring accuracy of laser gyro and accelerometer, further affected the service precision of Inertial Measurement Unit.Meanwhile, Temperature error model under the steady temperature environment of what traditional LIMU temperature calibration method obtained is limited number temperature spot, need to obtain continuous model by the method for sectional linear fitting is approximate, and this has brought larger approximate error to Temperature error model.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, the high-precision temperature scaling method of a kind of laser gyroscope inertia measurement unit is provided, the method has precision feature high and simple to operate, has greatly improved the service precision of LIMU under varying temperature environment.

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

(1) by laser gyroscope inertia measurement cellular installation on the three-axle table with incubator, setting warm the temperature inside the box is T _mbe 20 ℃～30 ℃, under LIMU works on power state, be incubated 6～8 hours;

(2) utilize three-axle table to carry out dynamic rotary rating test to LIMU, rotate three-axle table and successively the X-axis of LIMU, Y-axis, Z axis are overlapped with the Z axis of turntable, all the other diaxons, in surface level, make three-axle table with angular speed ω in each position ₀clockwise, the counterclockwise each rotating 360 degrees of both direction of Z axis around geographic coordinate system, records LIMU output data;

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

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

(5) be set up each axle output data and rotational-angular velocity of the earth and the acceleration of gravity relation between projection components on each axle of LIMU according to everybody, on the basis of LIMU error mathematic model, adopt symmetric position error phase elimination, calculate the relevant error term of constant value drift, acceleration of laser gyro and accelerometer constant multiplier, accelerometer bias, accelerometer alignment error;

(6) rotation three-axle table makes tri-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 _lfor-40 ℃～-30 ℃, temperature retention time t _tbe 150～180 minutes, rate temperature change v _tbe 1～3 ℃/min, the temperature that incubator is set changes according to following rule: 1. at T _minsulation t _t; 2. with-v _tspeed from T _mbe cooled to T _l; 3. at T _linsulation t _t; 4. with v _tspeed from T _lbe warming up to T _h; 5. at T _hinsulation t _t; 6. with-v _tspeed from T _hbe cooled to T _m; 7. at T _minsulation t _t; Record LIMU output data, record the temperature data of laser gyro and accelerometer output simultaneously;

(7), according to the output data of LIMU record, calculate in temperature cycling test process and T _mthe departure that under isoperibol, laser gyro constant value drift and accelerometer bias produce, bring in the Temperature error model of laser gyro constant value drift and accelerometer bias, carry out linear fit with the temperature data of laser gyro and accelerometer output, calculate a temperature coefficient q of X, Y, tri-direction laser gyro constant value drifts of Z _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 are often 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 laser gyro constant value drift Temperature error model and accelerometer bias Temperature error model, as follows respectively:

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

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

Wherein,

for the laser gyro of i (i=x, y, z) direction inclined to one side in the normal value zero in m moment, D _i0for the laser gyro of i direction is at T _mnormal value zero when temperature is inclined to one side, with

for the laser gyro of i direction is in m moment the 1st road and the 2nd tunnel temperature output valve, with

for the laser gyro of i direction is in m-1 moment the 1st road and the 2nd tunnel temperature output valve,

for i directional acceleration meter is at the normal value biasing in m moment, S _i0for i directional acceleration meter is at T _mnormal value biasing when temperature,

with

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

Principle of the present invention is: adopt and system inherent error is separated to the strategy of demarcating with temperature error, make LIMU reach overall thermal equilibrium state by the measure of long-term heat preservation under certain temperature spot, on this basis, the LIMU scaling method combining by dynamic rotary and static 24 positions accurately obtain gyro constant multiplier, gyroscope constant value zero partially, add meter constant multiplier, add the system inherent error coefficients such as the normal value biasing of meter, change on gyroscope constant value zero partially and add and often count the value impact causing of setovering thereby eliminated high and low temperature; Again take the system inherent error coefficient under this isoperibol as basis, LIMU is carried out to high and low temperature cycle labeling test, by the continuous variation of environment temperature, motivate gyroscope constant value in LIMU zero partially and the dynamic temperature error of accelerometer bias, 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, temperature coefficient of accelerometer bias, secondary temperature coefficient and temperature variation rate coefficient; The method separates system inherent error under constant temperature with the error being caused by temperature variation, improve the stated accuracy of LIMU system inherent error under isoperibol, motivate system temperature error by environment temperature dynamic change simultaneously, simulate more really the environment for use of LIMU in Practical Project, greatly improved the service precision of LIMU under varying temperature environment.

The present invention's advantage is compared with prior art: the present invention is by the measure that LIMU is incubated for a long time in three-axle table incubator, system inherent error is separated to demarcation with temperature error, improve the stated accuracy of LIMU system inherent error under isoperibol, motivate system temperature error by the dynamic change of environment temperature simultaneously, take the inherent error coefficient under isoperibol as benchmark, calibrate the temperature error coefficient of the inclined to one side and accelerometer bias of the normal value zero of laser gyro in LIMU; The error model that the method is used meets the environment for use of LIMU in Practical Project more, thereby has greatly improved the service precision of LIMU under varying temperature environment.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of laser inertia measuring unit temperature calibration method of the present invention.

Fig. 2 is dynamic rotary rating test method schematic diagram of the present invention.

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

Fig. 4 is Temperature of Warm Case change curve schematic diagram of the present invention.

Embodiment

The present invention adopts and system inherent error is separated to the strategy of demarcating with temperature error, make LIMU reach overall thermal balance by the measure of long-term heat preservation under certain temperature spot, the scaling method Accurate Calibration that adopts dynamic rotary and static 24 positions to combine goes out gyro constant multiplier under this temperature spot, gyroscope constant value drift, the system inherent error coefficients such as accelerometer constant multiplier and accelerometer bias, recycle the inherent error coefficient of LIMU under this temperature spot, LIMU is carried out to height, low temperature cyclic test, further calibrate gyroscope constant value drift, the temperature error coefficient of accelerometer bias, comprise temperature coefficient one time, secondary temperature coefficient, thermograde coefficient and temperature variation rate coefficient be totally 30 temperature correlation coefficients.

As shown in Figure 1, the concrete implementation step of the present invention is as follows:

1, by laser gyroscope inertia measurement cellular installation on the three-axle table with incubator, setting warm the temperature inside the box is T _mbe 20 ℃～30 ℃, under LIMU works on power state, be incubated 6～8 hours;

2, utilize turntable to carry out dynamic rotary rating test to LIMU, rotating table overlaps the X-axis of LIMU, Y-axis, Z axis successively with the Z axis of turntable, and as shown in Figure 2, all the other diaxons, in surface level, make turntable with angular speed ω in each position ₀clockwise, the counterclockwise each rotating 360 degrees of both direction of Z axis around geographic coordinate system, records LIMU output data;

Model LIMU gyroscope error model equation is 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 in test, three direction gyros of x, y, z gather, 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(i, j=x, y, z) is the relevant error coefficient of acceleration, A _x, A _y, A _zbe respectively the specific force of three direction inputs of x, y, z, M _ij(i, j=x, y, z) is gyro misalignment coefficient, ω _x, ω _y, ω _zbe respectively three direction input angular velocities of x, y, z.

Rotating table overlaps the X-axis of LIMU with the Z axis of three-axle table, Y-axis and Z axis, in surface level, make turntable with angular speed ω ₀the Z axis of platform of rotating turns clockwise 360 °, and as shown in Fig. 2 (a), another mistake hour hands rotating 360 degrees, as shown in Fig. 2 (b), obtains the output of three direction gyros 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 direction gyro gathers while representing to be rotated counterclockwise,

three pulses that direction gyro gathers while representing to turn clockwise, g represents acceleration of gravity,

for the Z axis component of rotational-angular velocity of the earth under local Department of Geography,

for the Y-direction component of rotational-angular velocity of the earth under local Department of Geography.

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

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

In situation that the X-axis of LIMU is overlapped with the Z axis of three-axle table, 0～360 ° of gyro output data suitable, that be rotated counterclockwise is carried out integration, establishes 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 to (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 axis of three-axle table and carry out situation suitable, that be rotated counterclockwise for Y-axis and the Z axis of LIMU, obtaining (7)～(8) formula,

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

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

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 meanwhile, 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 to carry out symmetrical 24 position static demarcating tests to LIMU, rotation three-axle table makes tri-coordinate axis of XYZ of LIMU overlap with local geographic coordinate system, then revolving-turret successively, the sensing of tri-coordinate axis of XYZ of LIMU is changed, rotate and will obtain 24 diverse locations for 24 times, on each position, record the output data of 3～5 minutes LIMU; As shown in Figure 3, concrete steps are as follows in concrete 24 positions:

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

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

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

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

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

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

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

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

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

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

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

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

5, be set up each axle output data and rotational-angular velocity of the earth and the acceleration of gravity relation between projection components on each axle of LIMU according to everybody, on the basis of LIMU error mathematic model, adopt symmetric position error phase elimination, calculate the relevant error term of constant value drift, acceleration of laser gyro and accelerometer constant multiplier, accelerometer bias, accelerometer alignment error;

In 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, be illustrated in the output of i direction gyro under m position; (13)～(16) formula is added to (17) formula that obtains,

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

Wherein,

represent the cumulative of i direction gyro output data, in like manner, after being added for the output of 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, to meet 8 positions of symmetry that the sky of the x axle of LIMU and geographic coordinate system overlaps to axle, in like manner, for 9～16 positions, to meet 8 positions of symmetry that the sky of the Y-axis of LIMU and geographic coordinate system overlaps to axle, 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 to meet 8 positions of symmetry that the sky of the Z axis of LIMU and geographic coordinate system overlaps to axle, can obtain (21)～(22) two formulas, $F_i^{50}=(F_i^{17}+F_i^{18}+F_i^{19}+F_i^{20})/4,$ $F_i^{60}=(F_i^{21}+F_i^{22}+F_i^{23}+F_i^{24})/4,$

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

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

By (17)～(22) formula, bring gyro constant multiplier and the alignment error obtained into, can calculate the inclined to one side D of normal value zero of gyro _i0with relevant with g coefficient D _ij(i, j=x, y, z), D _ijrepresent the coefficient between 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, "+" in the upper right corner represents to ask the generalized inverse of matrix; So far, obtain the relevant all error coefficients of gyro in 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 in test, three directional acceleration meters of x, y, z gather, 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(i, j=x, y, z) is accelerometer alignment error coefficient, A _x, A _y, A _zbe respectively the specific force of three direction inputs of x, y, 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, represent i directional acceleration meter after 1～4 position output data accumulation divided by 4 averages that obtain; 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, as 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, calibrate all error coefficients of accelerometer in LIMU, comprised accelerometer constant multiplier, accelerometer bias and accelerometer alignment error.

6, rotation three-axle table makes tri-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 _lfor-40 ℃～-30 ℃, temperature retention time t _tbe 150～180 minutes, rate temperature change v _tbe 1～3 ℃/min, the temperature that incubator is set changes according to following rule: 1. at T _minsulation t _t; 2. with-v _tspeed from T _mbe cooled to T _l; 3. at T _linsulation t _t; 4. with v _tspeed from T _lbe warming up to T _h; 5. at T _hinsulation t _t; 6. with-v _tspeed from T _hbe cooled to T _m; 7. at T _minsulation t _t; As shown in Figure 4, record LIMU output data, record the temperature data of laser gyro and accelerometer output simultaneously;

7,, according to the output data of LIMU record, calculate in temperature cycling test process and T _mthe departure that under isoperibol, laser gyro constant value drift and accelerometer bias produce, bring in the Temperature error model of laser gyro constant value drift and accelerometer bias, 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 of accelerometer bias totally 30 coefficients;

Described Temperature error model comprises laser gyro constant value drift Temperature error model and accelerometer 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,

for the laser gyro of i (i=x, y, z) direction inclined to one side in the normal value zero in m moment, D _i0for the laser gyro of i direction is at T _mtime normal value zero inclined to one side,

with

for the laser gyro of i direction is in m moment the 1st road and the 2nd tunnel temperature output valve,

with

for the laser gyro of i direction is at m-1 moment the 1st road and the 2nd tunnel temperature output valve, 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 at the normal value biasing in m moment, S _i0for i directional acceleration meter is at T _mtime the biasing of normal value,

with

be respectively i directional acceleration meter at the temperature output valve in m moment and m-1 moment, e _i1～e _i3be followed successively by a temperature coefficient, secondary temperature coefficient and the thermograde coefficient of i directional acceleration meter.The normal value zero that formula (37) has represented gyro under temperature variations partially and T _mthe relation of normal value in constant temperature situation zero between partially, formula (38) has represented normal value biasing and the T of accelerometer under temperature variations _mrelation between normal value biasing in 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

for the output that under temperature variation environment, i direction gyro gathered in the m moment, N _i0for T _mi direction gyro output under isoperibol, can be by the 1. stage T in the 6th step _minsulation t _tthe gyro data of exporting in process is averaging and obtains;

for i directional acceleration meter under temperature variation environment

The output gathering in the m moment, N _i0for T _mi directional acceleration meter output under isoperibol, can be by the 1. stage T in the 6th step _minsulation t _tthe accelerometer data of exporting in process is averaging and obtains; 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 in LIMU, Y, tri-direction laser gyro constant value drifts of Z _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 are often worth a temperature coefficient e of biasing _i1, secondary temperature coefficient e _i2with temperature variation rate coefficient e _i3totally 30 coefficients, complete the temperature calibration of laser gyroscope inertia measurement unit.

Non-elaborated part of the present invention belongs to those skilled in the art's known technology.

Claims (1)

1. a temperature calibration method for laser gyroscope inertia measurement unit, is characterized in that performing step is as follows:

(1) laser gyroscope inertia measurement unit (LIMU) is arranged on the three-axle table with incubator, setting warm the temperature inside the box is T _mbe 20 ℃～30 ℃, under LIMU works on power state, be incubated 6～8 hours;

(2) utilize three-axle table to carry out dynamic rotary rating test to LIMU, rotate three-axle table and successively the X-axis of LIMU, Y-axis, Z axis are overlapped with the Z axis of three-axle table, all the other diaxons, in surface level, make three-axle table with angular speed ω in each position ₀clockwise, the counterclockwise each rotating 360 degrees of both direction of Z axis around geographic coordinate system, records LIMU output data;

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

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

(5) be set up each axle output data and rotational-angular velocity of the earth and the acceleration of gravity relation between projection components on each axle of LIMU according to everybody, on the basis of LIMU error mathematic model, adopt symmetric position error phase elimination, calculate the relevant error term of constant value drift, acceleration of laser gyro and accelerometer constant multiplier, accelerometer bias, accelerometer alignment error;

(6) revolving-turret makes tri-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 _lfor-40 ℃～-30 ℃, temperature retention time t _tbe 150～180 minutes, rate temperature change v _tbe 1～3 ℃/min, the Temperature of Warm Case that three-axle table is set changes according to following rule: 1. at T _minsulation t _t; 2. with-v _tspeed from T _mbe cooled to T _l; 3. at T _linsulation t _t; 4. with v _tspeed from T _lbe warming up to T _h; 5. at T _hinsulation t _t; 6. with-v _tspeed from T _hbe cooled to T _m; 7. at T _minsulation t _t; Record LIMU output data, record the temperature data of laser gyro and accelerometer output simultaneously;

(7) according to the output data of LIMU record, calculate in temperature cycling test process with TM isoperibol under the departure that produces of laser gyro constant value drift and accelerometer bias, bring in the Temperature error model of laser gyro constant value drift and accelerometer bias, carry out linear fit with the temperature data of laser gyro and accelerometer output, calculate a temperature coefficient q of X, Y, tri-direction laser gyro constant value drifts of Z _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 are often 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;

Described Temperature error model comprises laser gyro constant value drift Temperature error model and accelerometer bias Temperature error model, as follows respectively:

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

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

Wherein,

for the laser gyro of i (i=x, y, z) direction inclined to one side in the normal value zero in m moment, D _i0for the laser gyro of i direction is at T _mnormal value zero when temperature is inclined to one side,

with for the laser gyro of i direction is in m moment the 1st road and the 2nd tunnel temperature output valve,

with

for the laser gyro of i direction is in m-1 moment the 1st road and the 2nd tunnel temperature output valve,

for i directional acceleration meter is at the normal value biasing in m moment, S _i0for i directional acceleration meter is at T _mnormal value biasing when temperature, T _i ^mand T _i ^m-1be respectively the temperature output valve of i directional acceleration meter in m moment and m-1 moment; e _i1～e _i3be followed successively by a temperature coefficient, secondary temperature coefficient and the temperature variation rate coefficient of i directional acceleration meter;

The normal value zero that formula (37) has represented gyro under temperature variations partially and T _mthe relation of normal value in constant temperature situation zero between partially, formula (38) has represented normal value biasing and the T of accelerometer under temperature variations _mrelation between normal value biasing in 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

for the output that under temperature variation environment, i direction gyro gathered in the m moment, N _i0for T _mi direction gyro output under isoperibol, by the 1. stage T in the 6th step _minsulation t _tthe gyro data of exporting in process is averaging and obtains;

for the output that under temperature variation environment, i directional acceleration meter gathered in the m moment, N _i0for T _mi directional acceleration meter output under isoperibol, by the 1. stage T in the 6th step _minsulation t _tthe accelerometer data of exporting in process is averaging and obtains; All temperatures coefficient of gyro and accelerometer are obtained in through type (39)～(40),

$\left[\begin{array}{c}{q}_{i1}\\ q_{i2}\\ .\\ .\\ .\\ q_{i7}\end{array}\right]={\left[\begin{array}{ccccccc}{T}_{i1}^1& T_{i2}^1& {\left(T_{i1}^1\right)}^2& {\left(T_{i2}^1\right)}^2& T_{i1}^1-T_{i2}^1& T_{i1}^1-T_{i1}^0& T_{i2}^1-T_{i2}^0\\ T_{i1}^2& T_{i2}^2& {\left(T_{i1}^2\right)}^2& {\left(T_{i2}^2\right)}^2& T_{i1}^2-T_{i2}^2& T_{i1}^2-T_{i1}^1& T_{i2}^2-T_{i2}^1\\ .& & & & & & .\\ .& & & ...& & & .\\ .& & & & & & .\\ T_{i1}^P& T_{i2}^P& {\left(T_{i1}^P\right)}^2& {\left(T_{i2}^P\right)}^2& T_{i1}^P-T_{i2}^P& T_{i1}^P-T_{i1}^{P-1}& T_{i2}^P-T_{i2}^{P-1}\end{array}\right]}^{+}\left[\begin{array}{c}{D}_i^1-D_{i0}\\ D_i^2-D_{i0}\\ .\\ .\\ .\\ D_i^P-D_{i0}\end{array}\right]---\left(39\right)$

$\left[\begin{array}{c}{e}_{i1}\\ e_{i2}\\ e_{i3}\end{array}\right]={\left[\begin{array}{ccc}{T_i}^1& {\left({T_i}^1\right)}^2& {T_i}^1-{T_i}^0\\ {T_i}^2& {\left({T_i}^2\right)}^2& {T_i}^2-{T_i}^1\\ .& .& .\\ .& .& .\\ .& .& .\\ {T_i}^P& {\left({T_i}^P\right)}^2& {T_i}^P-{T_i}^{P-1}\end{array}\right]}^{+}\left[\begin{array}{c}{S}_i^1-S_{i0}\\ S_i^2-S_{i0}\\ .\\ .\\ .\\ S_i^P-S_{i0}\end{array}\right]---\left(40\right)$

So far, calibrated a temperature coefficient q of X in LIMU, Y, tri-direction laser gyro constant value drifts of Z _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 are often worth a temperature coefficient e of biasing _i1, secondary temperature coefficient e _i2with temperature variation rate coefficient e _i3totally 30 coefficients, complete the temperature calibration of laser gyroscope inertia measurement unit.

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