RU2566427C1 - Method of determination of temperature dependences of scaling factors, zero shifts and array of orientation of axes of sensitivity of laser gyroscopes and pendulum accelerometers as part of inertial measuring unit at bench tests - Google Patents

Abstract

FIELD: instrument making.

SUBSTANCE: invention can be used for determination of temperature dependences of characteristics of the three-axis laser gyroscope (LG) and the pendulum accelerometers (PA) as a part of the inertial measuring units (IMU). At the stand IMU with three-axis LG and three PAs, fitted with rotation sensors, at each step of measurements the amount of impulses for each of three LG rotation sensors is determined which is proportional to the projection of LG rotation angle vector per one step of measurements per each of three axes of LG sensitivity, averages per one step of measurements of values of voltage at the output of three PAs proportional to projections of the vector of imaginary linear acceleration to the axes of sensitivity of PAs , and averages per one step of measurements of temperature in each of three rotation sensors of three-axis LG and three PAs are determined, using which the temperature dependences of all scaling factors of LG and PA are determined.

EFFECT: expansion of functional capabilities.

2 dwg

Description

The invention relates to the field of instrumentation, in particular to inertial navigation systems, and can be used to determine the temperature dependences of the characteristics of a triaxial laser gyroscope (LG) and pendulum accelerometers (MA) as part of an inertial measuring unit (IIB) during bench tests, in particular scale factors LG and MA rotation sensors, LG and MA rotation sensors zero rotations, LG and MA sensitivity axis matrices in the orthogonal coordinate system, rigidly associated with the IIB corps.

The known method [RU 2488776 C1, G01C 25/00, 07/27/2013], which consists in calibrating the systematic values of the parameters of the error model of a triaxial laser gyroscope, including the systematic components of the bias of zeros, and the calibration of the bias of the zeros of triaxial laser gyroscopes with one common vibrator is not according to direct readings of triaxial laser gyroscopes - increments of the projection integrals of the absolute angular velocity vector on the sensitivity axis, and from the resulting error in determining spatial orientations and by the strapdown inertial attitude control system based on the three-axis laser gyro with a single common vibrator.

The disadvantage of this method is its relatively narrow scope.

The closest in technical essence to the proposed one is the method [RU 2505785 C1, G01C 21/24, 01/27/2014], which includes measurements of the apparent accelerations of a carrier object moving in inertial space and a detachable object rigidly connected with it, made by accelerometers of the reference inertial navigation system of the object -carrier in the base inertial coordinate system (BISC) and accelerometers of the driven inertial navigation system of the separated object in the instrument inertial coordinate system (PISC), which is formed by E sensitivity accelerometers driven ANN transmission with a certain periodicity measurements accelerometers reference ANN carrier in a computing device (slave) separated object, wherein during the movement, after a certain time t _i, the measurements accelerometers reference ANN and driven ANN accumulate apparent velocity before achieving vector module apparent velocity obtained by readings of the accelerometers driven ANN setpoint, at which point t _{i + 1} is fixed in a detachable VU object components century Hur apparent velocity accumulated in the interval [t _i, t _{i + 1]} on indications reference ANN and driven INS, according to these data is determined and stored in the slave detachable object vector module error apparent velocity caused by measurement errors of the driven inertial navigation system and the relative projections of three apparent velocity vectors, formed according to the readings of each individual accelerometer of the driven ANN, onto the unit of apparent velocity accumulated from the readings of the accelerometers of the reference ANN, repeat such actions at least it at two intervals active movement, characterized by mutually non-collinear directions accumulated on them and on the first interval vectors apparent velocity, according to indications of accelerometers reference INS of the carrier facility and the driven ANN discharge the objects accumulated on at least one portion of the motion [t ₁ ^n, t ₂ ^{n] is} characterized by small values of accelerations along the axes of sufficient duration and bisque portion define a discharge VU object errors apparent velocity along the axes of sensitivity of each accelerometer in home ANN caused by the combined influence of measurement errors of the INS error value of each accelerometer is divided by the value of the integral of the influence function measurement error corresponding accelerometer, independent of the overload on the error accumulated in the interval [t ₁ ^n, t ₂ ^n] along the sensitivity axis of the accelerometer apparent speed, thereby determine and remember the parameters of the measurement errors of each accelerometer, independent of overload, from the stored errors of the modules of the measured apparent speed and obtained at least at three intervals of active movement, characterized by significant overloads, subtract the results of multiplying the error parameter values independent of the overload by the integrals of the function of the influence of this parameter of each accelerometer of the driven ANN on the apparent velocity module error accumulated over the corresponding interval active motion, and thereby determine the values of the right-hand sides of the system of linear equations for the parameters of the measurement errors of the accelerometers, depending on loadings, solve the linear system, determine from it and store the values of the error parameters of the measurement of accelerometers depending on the overload, using the found values independent of and depending on the overload of the error parameters of each accelerometer of the slave ANN, specify the current values of apparent accelerations obtained from these accelerometers and use them for numerical real-time integration of the basic equation of inertial navigation of the navigation path of the separated object.

The disadvantage of the closest technical solution is its relatively narrow scope, since the known method, although it allows you to determine the model parameters of the measurement error of measuring instruments of an inertial navigation system, but does not allow to determine the temperature dependences of the characteristics of a triaxial laser gyroscope (LG) and pendulum accelerometers (MA) as part of an inertial measuring unit (IIB), in particular, scale factors of LG and MA rotation sensors, sensor zero offsets the rotation of LG and MA, matrices of the directing cosines of the sensitivity axes of LG and MA in the orthogonal coordinate system, rigidly connected with the ISS body.

The problem to which the invention is directed is to expand the scope.

The required technical result is to expand the scope by introducing an additional arsenal of technical means (method operations) that determine the temperature dependences of the characteristics of a triaxial laser gyroscope and pendulum accelerometers as part of an inertial measuring unit.

The problem is solved, and the required technical result is achieved in a method based on the fact that an inertial measuring unit with a triaxial laser gyroscope and three pendulum accelerometers are installed on the bench, the sensitivity axes of which are oriented in the direction of the corresponding axes of the inertial measuring unit’s own coordinate system, for which the only temperature of the laser gyroscope is known matrix orientation of the sensitivity axes of rotation sensors in their own system the coordinates of the inertial measuring unit, at each measurement step, determine the number of pulses for each of the three sensors of rotation of the laser gyroscope, proportional to the projection of the vector of the angle of rotation of the laser gyroscope per measurement cycle on each of the three axes of sensitivity of the laser gyroscope, determine the average voltage values per measurement step at the output of each of the three pendulum accelerometers proportional to the projections of the apparent linear acceleration vector on the sensitivity axis of the pendulum accelerometers, and average temperature measurements for each of the three rotation sensors of a triaxial laser gyroscope and three pendulum accelerometers, which are used to determine the temperature dependences of the scale coefficients of the rotation sensors of the laser gyroscope separately for each mode “+” and “-” and for two ranges of angular velocities: a range of "low" (H) angular velocities, lower than the value corresponding to the amplitude of the frequency stand, and a range of "high" (B) angular velocities exceeding x such a quantity, from the relations

where α = x, y, z are the sensitivity axes of the rotation sensors of a triaxial laser gyro; Tq _α is the current temperature measured in the corresponding rotation sensor of the laser gyroscope, T ₀ is the fixed temperature value equal to 25 ° С, the temperature dependences of the zero displacements for each rotation sensor of the triaxial laser gyroscope are determined separately for the magnetic (M) component that changes sign during the transition from one mode to another, and a non-magnetic (NM) component, independent of the mode, from the relations

temperature dependences of scale factors and displacements of zeros of pendulum accelerometers from the relations

where α = x, y, z - axis sensitivity MA; Ta _α is the current temperature measured in the corresponding pendulum accelerometer, the temperature dependences of the off-diagonal elements of the matrices of the guide cosines of the sensitivity axes of the triaxial laser gyroscope and pendulum accelerometers in the own coordinate system of the inertial measuring unit

from the relations

where Tq is the temperature of the laser gyroscope averaged over all three rotation sensors,

and the diagonal elements of the matrices of the directing cosines of the sensitivity axes of the triaxial laser gyroscope and pendulum accelerometers in the inertial coordinate system of the inertial measuring unit are determined through off-diagonal ones, based on the normalization conditions in rows

The drawings show:

in FIG. 1 - bench coordinate system (initial position);

in FIG. 2 - the position of the bench coordinate system of the inertial measuring unit during testing.

The proposed method for determining the temperature dependences of scale factors, zero offsets, and orientation axes of the sensitivity axes of a triaxial laser gyroscope and pendulum accelerometers as part of an inertial measuring unit during bench tests is implemented as follows.

The aim of the present invention is to determine the temperature dependences of the characteristics of a triaxial laser gyroscope (LG) and pendulum accelerometers (MA) as part of an inertial measuring unit (IIB):

- scale coefficients of rotation sensors LH and MA;

- zero offsets of the rotation sensors LH and MA;

- matrices of the directing cosines of the sensitivity axes of the LG and MA in the orthogonal coordinate system - the coordinate system (SSC) rigidly connected to the IIB housing.

The sensitivity axes of the three LG rotation sensors and three MA are oriented in the direction of the corresponding axes of the SSC with some errors to be determined.

Each of the three rotation sensors in the LG and each of the three MAs is equipped with a temperature sensor that measures temperature. The triaxial LG operates alternately on two orthogonal modes Μ = "+" and Μ = "-"; Periodic switching from one mode to another and vice versa reduces the influence of the magnetic component of the zero offset (zero drift) on the measurements of the angular velocity of rotation.

In the technological mode, at each cycle, the following data is taken from LH and MA:

- the number of pulses for each of the 3 LG rotation sensors, proportional to the projection of the vector of the rotation angle of the LG for one data transmission clock on each of the 3 axes of LG sensitivity, moreover, if the angle accumulated on the axis in one cycle is not a multiple of an integer number of pulses, then information distortion does not occur, since the “residual” angle goes to the next beat; in addition, in this mode, every ΝΜ clock cycles, a transition from one mode to another is realized;

- average values of the voltage at the output of three MAs per cycle, proportional to the projections of the apparent linear acceleration vector on the sensitivity axis of the MA.

- average temperature values per cycle for each of the three LG rotation sensors and three MAs;

The temperature dependences of the scale coefficients of LG rotation sensors are close to linear and are determined separately for each “+” and “-” mode and for two ranges of angular velocities: a range of “low” (Η) angular velocities, lower than the value corresponding to the amplitude of the frequency stand, and the range of "high" (B) angular velocities exceeding such a value

where α = x, y, z are the sensitivity axes of the LG rotation sensors; Tq _α is the current temperature measured in the corresponding LG rotation sensor, T ₀ is a fixed temperature value equal to 25 ° С.

The displacements (drift) of zeros for each LG rotation sensor contain two components: magnetic (M), which changes sign when switching from one mode to another, and non-magnetic (NM), which is independent of the mode. The temperature dependences of each of these components of the drift are determined in the form of second-order polynomials

The temperature dependences of the scale factors and displacements of the zeros of the MA are determined in the form of third-order polynomials

where α = x, y, z - axis sensitivity MA; Ta _α is the current temperature measured in the corresponding MA.

Temperature dependences of the off-diagonal elements of the matrices of the directing cosines of the sensitivity axes of the LG (q) and MA (a) in the SIRS

are defined as polynomials of the first order

where Tq is the LG temperature averaged over all three rotation sensors.

The diagonal elements of the matrices (6), (7) are determined in terms of off-diagonal elements, based on the normalization conditions for the rows

To achieve this goal, it is necessary to experimentally determine the coefficients of polynomials (1) - (5), (8), (9) from the data taken from the ISS.

As initial data, there is a matrix of guide cosines of the LG sensitivity axes in the SIRS under normal climatic conditions (GCC)

and the temperature value Tq _NKU , the average for all three sensors of rotation of the LG, which corresponds to this matrix.

Here α = x, y, z are the axis of sensitivity of the LG; β _svsk = X _svsk , Y _svsk , Z _svsk - axis of _SSC .

To achieve this goal, experiments are carried out using a high-precision biaxial test bench equipped with a heat and cold chamber (CTX). The normal to the installation platform of the stand coincides with the axis 1 of the stand. The axis 2 of the stand is orthogonal to axis 1 and is horizontal. The stand is installed in such a way that at zero angles set for both axes of the stand, axis 1 is directed upward and axis 2 is directed north. Errors in the installation of the stand should be identified and taken into account when determining the desired characteristics.

We introduce into consideration an orthogonal bench coordinate system (CSC) X _st Y _st Z _st rigidly connected with the installation platform of the stand, the axes of which are oriented in the initial position of the stand as follows (Fig. 1):

- the axis of X _st coincides with the axis 2 of the stand (oriented north);

- the axis of the Y _article coincides with the axis 1 of the stand (oriented up);

- the axis of Z _article complements the axis of X _article and Y _article to the right three (oriented east).

не совпадает с осью Y_ст и, в начальном положении стенда, проецируется на оси Х_ст, Y_ст, Z_ст какDue to errors in the installation of the stand, the vector of the local vertical $$\overline{G}$$

does not coincide with the axis of the Y _article and, in the initial position of the stand, is projected on the axis of the X _article , Y _article , Z _article as

where [·] ^T is the transpose of the vector [·].

в исходном положении стенда проецируется на оси Х_ст, Y_ст, Z_ст какEarth angular velocity vector $$\overline{\Omega }$$

in the initial position of the stand is projected on the axis of the X _article , Y _article , Z _article as

и $$\overline{\Omega }$$

выражаются через направляющие косинусы в видеVector projections $$\overline{G}$$

and $$\overline{\Omega }$$

expressed through guide cosines in the form

where G and Ω are the known values of the acceleration of gravity at the point of measurement and the angular velocity of rotation of the Earth,

, Ω_i, i=1, 2, 3 подлежат экспериментальному определению, при этомValues $$b_{G_i}$$

, Ω _i , i = 1, 2, 3 are subject to experimental determination, while

The ISS with the help of special equipment is placed and rigidly fixed on the installation platform of the stand in such a way that the axes of the ISS ISS are oriented along the corresponding axes of the ISS, although, strictly speaking, they do not coincide with them.

и $$\overline{\Omega }$$

на оси СТСК.Tests are carried out at 12 different positions of the HSCC shown in FIG. 2, wherein the position Y _a corresponds to the initial position shown in FIG. 1. Under each of these positions in FIG. 2 shows the values of the projections of the vectors $$\overline{G}$$

and $$\overline{\Omega }$$

on the axis of the STSK.

The tests are carried out sequentially at several specified temperatures in the performance characteristics of the stand

overlapping a given temperature range.

The sequence of experiments.

For each of the temperatures in the CTX stand (21), the following sequence of actions is performed.

1. The conclusion of the CTX at a given temperature.

2. Exposure of the ISS at this temperature for a predetermined time, depending on the weight of the equipment and the ISS and guaranteeing the achievement of the specified temperature in the CTX by all components of the ISS.

3. Turn on the ISS, set up the stand platform in the initial position Y _a and take data from the LG rotation sensors in this fixed position for 1 hour in order to determine the values of magnetic and non-magnetic drift.

4. Rotations of the bench mounting platform relative to each of the STSK axes by an angle of ± 720 ° (2 full turns to one or the other side) at 2 speeds ("low" and "high") and 2 LG modes = "+ "And" - "

The rotations along the axes X _st , Z _st are performed relative to the axis 2 of the stand, and Y _a , and along the axis Y _st - relative to the axis 1. When rotating about the axes X _st , Y _{st, the} initial position of the STSK is the position Y _a , and during rotations about the axis Z _article - the position of X _a .

The data taken during such rotations are used to determine the values of the scale factors of the LG rotation sensors, as well as the matrices of the directing cosines of the LG sensitivity axes in the CSC and then in the CSC.

For each set of 6 rotations with fixed values of parameters (22), the average temperature is determined for all three LG sensors.

и проекций G₁, G₂, G₃ вектора местной вертикали $$\overline{G}$$

на оси СТСК для ее нулевого положения (фиг. 1), а затем, с учетом этих проекций - значений масштабных коэффициентов и смещений нуля МА, а также матриц направляющих косинусов осей чувствительности МА в СТСК и затем в СВСК.5. The sequential installation of the ISS in 12 fixed positions shown in Figure 2. Data taken from LG and MA in each of these positions are used to determine the projections Ω ₁ , Ω ₂ , Ω ₃ of the angular velocity vector of the Earth $$\overline{\Omega }$$

and projections G ₁ , G ₂ , G ₃ local vertical vector $$\overline{G}$$

on the CSCS axis for its zero position (Fig. 1), and then, taking into account these projections, the values of the MA scale factors and zero offsets, as well as the matrices of the directing cosines of the MA sensitivity axes in the CSCS and then in the CSCS.

Processing of measurement results.

Processing the data obtained at each fixed temperature T _{ktx j} , j∈J _ktx (21) is as follows.

The measurement data obtained in paragraph 4 at each fixed temperature in the CTX of the stand T _{ktx j} , j∈J _ktx (21) are a set of sums of pulses from each LG rotation sensor α = x, y, z during rotations in opposite directions relative to three axes of the CSC with four combinations of parameter values (22)

as well as the average temperatures at each of these sensors for each of these rotations:

where α = x, y, z is the index of the axis of sensitivity of the LG,

β _article = X _article , Y _article , Z _article - index of the axis of the CSC, relative to which the rotation was performed; the plus or minus sign in front of this index indicates the direction of rotation;

For each set of 6 rotations performed with four combinations (22) of the values of the parameters ω and M, the following are calculated:

- LH scale factors (in arc.s / impulse) in the form

Where

- matrix elements

guide cosines of the axes of sensitivity of the LG in the STSK in the form

- the average temperature for each of the rotation sensors in each set of 6 rotations according to the formula

which corresponds to the calculated value (26) of the scale factor of this sensor;

- the average temperature value for all three LG rotation sensors

which corresponds to the calculated elements of the matrix of the orientation of the axes of sensitivity of the LG in the STSK.

For each rotation sensor α = x, y, z for each of the four sets of operating points

linear interpolation is performed using the least squares method. As a result of this, the coefficients of polynomials (1) are determined.

For each off-diagonal element of the matrix of the guiding cosines of the LG sensitivity axes in STSK

by set of operating points

j = 1,2, ... N _kth , ω = ω _Η , ω _Β ; Μ = "+", "-"

linear interpolation is performed using the least squares method. As a result of this, the coefficients of the first-order polynomial are determined

approximating the temperature dependence of each such element.

The temperature dependences of the diagonal elements of matrix (33) are found from the normalization condition along the line

Relations (35), (36) determine the temperature dependence of the orientation matrix of the LG sensitivity axes in the HSC

Using a temperature-dependent (37), this matrix is computed at temperatures Tq = TQ _CLE

The given matrix (12) and the calculated matrix (38) describe the orientation of the LG sensitivity axes in two different orthogonal coordinate systems SSC and SSC at the same LG temperature. Therefore, they can be used to calculate the temperature-independent orientation matrix of the HSC relative to the HSS

At any arbitrary temperature Tq, the matrix of the directing cosines of the LG sensitivity axes in the SIRS is a product of matrices (37) and (39)

, для каждого из таких элементов согласно (31), (40) формируется совокупность рабочих точек (узлов аппроксимации)To calculate the coefficients of polynomials (8), approximating the thermal dependence of off-diagonal matrix elements $$\left[C{q}_{\alpha {\beta }_{\mathrm{from}\mathrm{at}\mathrm{from}\mathrm{to}}}\right]$$

, for each of such elements according to (31), (40), a set of operating points (approximation nodes) is formed

j = 1,2, ... Ν _ctx , ω = ω _Η , ω _B ; Μ = "+", "-"

and using the least squares method, the coefficients of these polynomials are determined.

The data obtained from the accelerometers in paragraph 2.5 at a fixed temperature T _{ktj j} in the KTX of the stand are measured for each of the 12 positions (Figure 2)

, где ψ ∈ Ψ $$\stackrel{\Delta }{=}$$

{Υ_а,Υ_б,…,Χ_Г} - совокупность положений стенда (42). При съеме данных в п. 2.5 ИИБ функционирует в квазистационарном температурном режиме, при котором величины масштабных коэффициентов и ориентацию осей чувствительности МА в СТСК можно считать неизменной.average values of voltages and temperatures taken from accelerometers α = x, y, z $$T{\mathrm{but}}_{j\alpha }^{\psi }$$

, where ψ ∈ Ψ $$\stackrel{\Delta }{=}$$

{Υ _a , Υ _b , ..., Χ _G } - a set of positions of the stand (42). When taking the data in Section 2.5, the ISS operates in a quasistationary temperature regime in which the magnitude of the scale factors and the orientation of the sensitivity axes of the MA in the STSC can be considered unchanged.

At each fixed temperature T _ktj in the KTX stand are determined:

(направляющего косинуса вектора $$\overline{G}$$

по отношению к вертикальной оси стенда) в виде- MA scale factors (in m / s ² / v) up to an unknown parameter $$b_{G_{\mathrm{one}}}$$

(directing cosine of the vector $$\overline{G}$$

in relation to the vertical axis of the stand) in the form

Where

, в частности, в соотношениях (44) - проекции G₁=G·b_G1;and the following indexation is adopted for the variables W: the upper index denotes a group of 4 positions of the device with the STSC axis pointing vertically oriented, the first character in the lower index indicates the set temperature in the CTX T _{ass j} , the second character indicates the sensitivity axis ΜΑ, the third symbol - on the axis of the SSCC, along which, using the operations of addition and subtraction, the effect of one specific projection of the vector $$\overline{G}$$

in particular, in relations (44), the projections G ₁ = G · b _G1 ;

по отношению к вертикальной оси стенда по данным, полученным при температуре Т_{ктх j} в КТХ стенда, вычисляется с использованием свойства (19) по данным, снятым с акселерометра, ось чувствительности которого направлена по оси z в виде:- estimate of the value of the directing cosine b _{G1 of the} vector $$\overline{G}$$

with respect to the vertical axis of the bench according to the data obtained at a temperature T _{ktj j} in the CTX of the stand, it is calculated using property (19) according to the data taken from the accelerometer, the sensitivity axis of which is directed along the z axis in the form:

- определена в (44), а

и

- вычисляются какWhere

is defined in (44), and

and

- are calculated as

- matrix elements

guide cosines of the axes of sensitivity of the LG in the STSK in the form

- the average temperature at each of the accelerometers α = x, y, z for all 12 positions (42)

for the subsequent approximation of the temperature dependences of the scale factors and the displacements of the zeros of the MA;

- average temperature across all three accelerometers

to which correspond the calculated elements of the matrix of the orientation of the axes of sensitivity of the MA in the CSC.

The orientation of the stand relative to the local vertical does not depend on the temperature in the CTX of the stand. Therefore, the estimates of the guiding cosine hgt should be averaged over all temperatures in the CTX of the stand (21)

The values of the MA scale factors at all temperatures (21) are calculated by formulas (43) - (46), (51).

For each ΜA α = x, y, z according to the set of operating points (interpolation nodes)

the least squares method determines the desired coefficients of the polynomial (4).

The displacements of the zeros of each MA α = x, y, z at each temperature in the CTX of the stand are calculated by the formulas

For each MA α = x, y, z according to the set of operating points (interpolation nodes)

the least squares method determines the desired coefficients of the polynomial (5).

на оси СТСК (фиг. 1). При съеме данных в п. 5 ИИБ функционирует в квазистационарном температурном режиме, при котором величины масштабных коэффициентов и ориентацию осей чувствительности ЛГ в СТСК можно считать неизменной. На фиг. 2 под каждым из этих положений показаны значения проекций этого вектора на оси СТСК. В каждом из положений ψ∈Ψ (42) при неподвижном состоянии прибора производится съем данных в течение двух полупериодов изменения моды ЛГ.The data obtained with LG in paragraph 5 in 12 positions (Fig. 2) at a fixed temperature T _{ct j} in the CTC of the stand are used to determine the estimates of the projections of the angular velocity vector of the Earth $$\overline{G}$$

on the axis of the STSK (Fig. 1). When taking the data in paragraph 5, the ISS operates in a quasistationary temperature regime, in which the magnitude of the scale factors and the orientation of the axes of sensitivity of the LG in the STSC can be considered unchanged. In FIG. 2, under each of these positions, the projection values of this vector on the CSCS axis are shown. In each of the positions ψ∈Ψ (42), when the device is stationary, the data is read during two half-periods of the LG mode change.

At each half-cycle with a constant LG mode for each of the LG rotation sensors α = x, y, z, the average values of the number of pulses per one transmission cycle are calculated, respectively

When determining these average values, the calculations do not include data for a fixed number N _{excluding the} first clock cycles in each half-period to exclude the influence of transients caused by switching of the LG mode.

, ψ∈Ψ, определяются значения температуры на каждом датчике вращения, усредненные по всем 12-ти положениямAccording to temperature measurements on rotation sensors at 12 positions

, ψ∈Ψ, the temperature values for each rotation sensor are determined, averaged over all 12 positions

For each of the positions (42), the angular velocity values measured on the LG sensitivity axes α = x, y, z are determined

,

- значения масштабного коэффициента для датчика вращения α=х, у, z, соответствующие моде «+» и моде «-», вычисленные по температуре $$T{q}_{j\alpha }$$

согласно первой и второй термозависимостям из (1);Where

,

- the values of the scale factor for the rotation sensor α = x, y, z, corresponding to the mode “+” and mode “-”, calculated by temperature $$T{q}_{j\alpha }$$

according to the first and second thermal dependences from (1);

Δt is the duration of the cycle of information retrieval from the LG.

Separately, for each of the 3 groups of positions with a vertical orientation corresponding to the CSCS axis (Fig. 2), estimates of the projections of the Earth's angular velocity vector on the CSCS axis Ω ₁ , Ω ₂ , Ω _{3 are} determined (Fig. 1):

- for a group of positions with a vertical orientation of the Xst axis in the form

where Δt is the duration of the cycle of information retrieval from LG;

,

,

- значения диагональных членов матрицы ориентации осей чувствительности ЛГ в СТСК, вычисленные согласно термозависимости (37) по температуре, осредненной по всем трем датчикам вращения ЛГ:

,

,

- the values of the diagonal members of the orientation matrix of the LG sensitivity axes in the CSC, calculated according to the temperature dependence (37) over the temperature averaged over all three LG rotation sensors:

- for a group of positions with a vertical orientation of the axis Y _article in the form

- for a group of positions with a vertical orientation of the axis Z _article in the form:

The orientation of the stand relative to the vector of the angular velocity of the Earth does not depend on the temperature in the CTX of the stand. Therefore, estimates of the projections of this vector on the HFS axis in its initial position should be averaged over all groups of positions at all temperatures (21)

where Ω - 15.04107 deg / s - the known value of the module of the vector of the angular velocity of rotation of the Earth.

The data obtained from LG rotation sensors in Sec. 2.3 are used to determine the coefficients of thermal dependences of magnetic and non-magnetic drifts (2), (3). The realizations taken at fixed temperature values in the CTX of the stand (21) consist of a sequence of time intervals with alternating values of the LG mode, and the mode “-” is established on the first such interval. For each m-th pair of successive intervals separately for the mode “+” and mode “-”, the average values of the number of pulses received from the rotation sensors α = x, y, z for one data acquisition cycle are determined

and average temperature values for each of these sensors:

as well as the overall average temperature for all three sensors and both LG modes

where j = 1,2, ..., Ν _CTX is the temperature index in the CTX of the stand;

m = 1, 2, ..., N _M is the index of a pair of intervals.

For each mth pair of intervals, the values of the magnetic and nonmagnetic components of zero drift are calculated by the formulas

,

- значения масштабного коэффициента для датчика вращения α=х, у, z, соответствующие моде «+» и моде «-», вычисленные по соответствующим значениям температуры

,

согласно первой и второй термозависимостям из (1) с коэффициентами, найденными выше;Where

,

- the values of the scale factor for the rotation sensor α = x, y, z, corresponding to the mode “+” and mode “-”, calculated from the corresponding temperature values

,

according to the first and second thermal dependences from (1) with the coefficients found above;

Ω _jα are the projections of the Earth’s angular velocity vector on the LG sensitivity axis α = x, y, z in position Y _a , calculated by the formulas

,

,

- элементы матрицы ориентации этих осей чувствительности ЛГ в СТСК, вычисленные при температуре $${\overline{T}}_{jm}$$

согласно найденной выше термозависимости матрицы ориентации этих осей в СТСК (37);Where

,

,

are the elements of the orientation matrix of these LG sensitivity axes in the HSC calculated at temperature $${\overline{T}}_{jm}$$

according to the temperature dependence of the orientation matrix of these axes found in STSK (37);

Ω ₁ , Ω ₂ , Ω ₃ - projection of the angular velocity vector of the Earth, calculated above.

Based on the combination of magnetic and non-magnetic drift values and the corresponding temperature values obtained above, for the magnetic and non-magnetic drift of each of the LG rotation sensors α = x, y, z, a set of operating points is formed:

j = 1, 2, ..., N _cth , m = 1,2, ..., Ν _Μ ,

by which the least coefficients of polynomials (2), (3) are determined by the least squares method.

Thus, due to the introduction of additional operations of the method, the required technical result is achieved, which consists in expanding the scope of the method, since it is possible to determine the temperature dependences of the characteristics of a triaxial laser gyroscope and pendulum accelerometers in an inertial measuring unit.

Claims (1)

A method for determining the temperature dependences of scale factors, zero offsets, and orientation axes of the sensitivity axes of laser gyroscopes and pendulum accelerometers as part of an inertial measuring unit during bench tests, based on measuring the parameters of the pendulum accelerometers, as well as processing the measurement results, characterized in that they install an inertial on the stand measuring unit with a triaxial laser gyroscope and three pendulum accelerometers equipped with sensors and rotations that are oriented in the direction of the corresponding axes of the inertial measuring unit’s own coordinate system, at each measurement step, determine the number of pulses for each of the three laser gyro rotation sensors proportional to the projection of the laser gyro rotation angle vector per measurement cycle on each of the three laser sensitivity axes gyroscope, determine the average voltage per output of three pendulum accelerometers, proportional to the projections vectors of apparent linear acceleration on the sensitivity axis of the pendulum accelerometers, and the average temperature values for each of the three rotation sensors of the triaxial laser gyroscope and three pendulum accelerometers, which determine the temperature dependences of the scale coefficients of the rotation sensors of the laser gyro for each mode + + "And" - "and for two ranges of angular velocities of the range of" low "(N) angular velocities less than the value corresponding to the amplitude Stand-frequency, and "high" range (B) of the angular velocity exceeding a value of ratios

where α = x, y, z are the sensitivity axes of the rotation sensors of the laser gyroscope; Tq _α is the current temperature measured in the corresponding rotation sensor of the laser gyroscope, T ₀ is a fixed temperature value equal to 25 ° C,
the temperature dependences of the zeros displacement for each rotation sensor of a laser gyroscope are determined from the relations containing magnetic (M), which changes sign when switching from one mode to another and nonmagnetic (NM), which is independent of the mode, components

temperature dependences of scale factors and displacements of zeros of pendulum accelerometers from the relations

where α = x, y, z are the sensitivity axes ΜΑ; Ta _α is the current temperature measured in the corresponding pendulum accelerometer,
temperature dependences of off-diagonal elements of matrices of guide cosines of sensitivity axes of a laser gyroscope and pendulum accelerometers

from the relations

where Tq is the temperature of the laser gyroscope averaged over all three rotation sensors,
and the diagonal elements of the matrices of the guiding cosines of the sensitivity axes of the laser gyroscope and pendulum accelerometers are determined through off-diagonal ones, based on the normalization conditions in rows

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