RU2727344C1 - Method for increasing calibration accuracy of unit of angular velocity micromechanical sensors - Google Patents

Abstract

FIELD: physics.SUBSTANCE: invention relates to navigation, navigation instruments, testing and calibration and can be used to calibrate sensors of strapdown inertial systems for orientation and navigation of aircraft, sea, ground and other mobile objects. Method comprises an initial platform display, a static experiment, with the platform stationary, successive rotation using the bench equipment at least on two non-parallel axes in the calibrated integrated data base basis, recording of the reading of the integrated data base on the channel of linear acceleration sensors (LAS) and readings of angular velocity sensors (AVS). By identifying proposed nonlinear mathematical model of AVS, zero angles of angular velocity sensor, matrix describing scale factors, cross links, non-linear coefficients are determined, for this purpose calibration program is developed. Program includes execution of a sequence of rotations and inclination angles of the platform in accordance with 6 specified experiments with duration of rotation and platform inclination time interval of about 3–4 minutes. Processing of obtained data includes selection of time interval with duration of about 2–3 minutes with established angular speed and inclination angles, calculation of ADC AVS codes average values, differentiation of goniometer readings and calculation of average values of angular velocities of table platform, calculation of average values of temperature sensors readings. Further, using certain algorithms, calibration factors are determined. According to the proposed method, estimation of scales and non-orthogonality angles is performed together with shifts of zeros. This ensures invariance of estimates of scale factors and angles of non-orthogonality with respect to shifts of zeros of the AVS and, accordingly, high accuracy, which is important for micromechanical angular velocity sensors with high level of instability of zero shifts.EFFECT: technical result is higher accuracy of calibration of scaling factors and angles of non-orthogonality of micromechanical angular velocity sensors.1 cl, 5 tbl, 1 dwg

Description

The invention relates to the field of navigation, navigation devices, testing and calibration, and can be used to calibrate the sensors of strapdown inertial attitude control and navigation systems of aircraft, sea, ground and other mobile objects. An integrated sensor unit (IDU) is a triple orthogonal angular velocity sensor (DUS) and a triple orthogonal linear acceleration sensor (DLU) mounted in a common housing, whose corresponding sensitivity axes are collinear. These blocks are also called inertial measurement modules (IMU).

The accuracy of inertial navigation and attitude control systems largely depends on the correct accounting for the systematic errors of gyroscopes detected by the calibration procedure. The use of a high-precision test bench allows us to hope for an improvement in the quality of calibration of micromechanical instruments of medium and low accuracy class. In this case, it is important to substantiate the mathematical model of measurements of the investigated sensors and the formation of the necessary set of experiments. The invention proposes to eliminate the harmful effect of residual zero compensation errors on errors in determining the non-orthogonality of the sensor sensitivity axes by increasing the information content of the experimental data. This is especially true for MEMS DUS.

There is a fast way to calibrate IMM [1]. In accordance with this method, the operator rotates the IMU in all directions without external equipment or with the help of equipment. The data taken at this time from the IMM allows one to determine 12 coefficients of the error models of the IMM sensors, including the drift velocities and scaling factors of the control system, zero signals and the scaling factors of accelerometers.

There is also known a method for calibrating the DUS as part of the strapdown inertial measuring modules (BIIM) [2], while using the signals of the two-component DUS and three one-component accelerometers, i.e. of the block of accelerometers that are part of the BIIM, the coefficients of the model of the angular velocity of the drift of each DUS, which depends and does not depend on linear overloads, are calibrated, as well as the angles of deviations of its two axes of sensitivity and the axis of angular momentum from their nominal directions, materialized by the mounting plane and the base direction on the body DUS.

The essence of the method is that with the help of a bracket and a rotary installation, the IMU is installed in 3 different fixed positions along the zenith angle (Θ = 0 °; Θ = 90 °), while the zenith angles are set according to the signals of the accelerometers and in each of them they are deployed IMI for azimuth angles close to the values of 0 °, 90 °, 180 °, 270 °. In all fixed positions, the DLS signals are determined by two components of the vector of the measured angular velocity of the Earth's rotation, they are stored, and then the results of measurements of the same name are added and subtracted for each measured component of the angular velocity and, according to the appropriate algorithms, the coefficients of the models of the angular velocities of the drift are determined, as well as the angles of inaccurate setting the axes of sensitivity and the vector of the angular momentum of the DUS. In this case, the signals from the accelerometer unit are used to determine the zenith angle and the deflector installation angle.

The disadvantage of this method is that it does not provide calibration modes of scale factors, does not fully ensure the determination of the angles of inaccurate installation of the measuring axes of one-component DUS based on fiber-optic, wave solid-state and other gyroscopes, three accelerometers, and also does not allow determining the angles of non-parallelism of the corresponding measuring axes of DUS and accelerometers.

The closest analogue to the claimed method is a method for calibrating the angular velocity sensors of a strapdown IMM [3], implemented in a known wide-range stand (for example, UPG-48), which provides approximately horizontal setting of the angular velocity vector with a fixed direction in space. With the help of bench equipment, the IMU is rotated sequentially around three approximately orthogonal IMU axes. During rotation, the IMM readings are recorded along the accelerometer channel, the DUS readings. According to the signals of the accelerometers, the angular velocity of the IMU is determined in the basis of the accelerometers. By identifying the mathematical model of the ADS, the zero signals of the ADS, the matrix describing the scale factors, cross-links, the orientation of the sensitivity axes of the ADS in the IMM, the matrix describing the effect of linear acceleration on the readings of the ADS are determined.

The disadvantage of all the above calibration methods is the need to precompensate for zero offsets. This leads to the propagation of offset compensation errors to errors in the identification of non-orthogonality angles and scale factors. Due to the high sensitivity of the estimates of nonorthogonality to zero offsets, their accuracy drops significantly.

The aim of the invention is to improve the accuracy of calibration of scale factors and angles of non-orthogonality of micromechanical DUS by eliminating the harmful effect of residual errors in zero compensation on errors in determining non-orthogonality by increasing the information content of experimental data.

This goal is achieved due to the fact that according to the claimed method for improving the calibration accuracy of the micromechanical angular velocity sensor unit, including the initial platform exposure, a static experiment with the platform stationary, rotation using bench equipment sequentially along at least two non-parallel axes in the basis of the calibrated IDU, in the rotation time is recorded by the readings of the IDS through the channel of the linear acceleration sensors (DLS), the readings of the angular velocity sensors (ADS), identifying the mathematical model of the ADS, determine the zero signals of the ADS, the matrix describing the scale factors, cross-links, additionally use a nonlinear model of the micromechanical ADS: u = K (ω) ω + С + е + F (ω),

where F (ω) is a vector of nonlinear functions of the form:

where: b _x , b _y , b _z are the nonlinearity coefficients of the functions ƒ,

K (ω) = DS (ω), ω = ω _c + ω _g , С ^T = [с _х с _у с _z ],

ω _c - vector of projections of angular velocities on the axis of the SC of the block due to the rotation of the table platform; ω _g - vector of projections of angular velocities due to the rotation of the Earth; С - vector of displacements of zeros of the DOS in code units; e - noise; K - matrix of calibration coefficients, taking into account the scales and angles of non-orthogonality: S - diagonal matrix of scale factors; D is a matrix of non-orthogonality angles, the development of a program for the automation of the calibration process, which includes the execution of a sequence of rotations and tilt angles of the platform in accordance with the 6 experiments indicated in Table 1, with a time interval duration with given parameters of rotations and tilt angles of the platform of about 3-4 minutes ...

The obtained data are processed, including the selection of a time interval of about 2-3 minutes with a steady angular velocity and tilt angles, the calculation of the average values of the ADC DUS codes, the differentiation of the goniometer readings and the calculation of the average values of the angular velocities of the table platform, three systems of equations are left to determine the calibration coefficients , each system contains six equations for measurements of the OLS signals:

For each CRS, five coefficients are determined, the vectors of which have the form:

The vector estimates of the coefficients are calculated using the least squares method. Calibration control according to experiments of rotations is carried out by evaluating the average values of angular velocities

Mathematical expectations and standard deviations of estimation errors are used for control:

The mathematical expectations of the estimation errors must be close to zero, the standard deviation of the estimation errors must be of the order of the standard deviation of the measurement noise.

The essence of the method for determining the calibration coefficients is described below.

We consider the calibration of a three-coordinate unit of angular velocity sensors using data from six rotations - three rotations separately along each of the three axes: X, Y, Z and three rotations along two axes: XY, YZ, XZ. Rotation of the block along two axes is provided by rotating the turntable of the stand along the outer vertical axis at the angles of inclination along the roll and pitch. Table 1 shows a set of rotations and tilt angles to ensure equal projections of the angular velocity 50 [deg / s] on the axis of the rectangular coordinate system (SC) of the block. Here the axes of the rectangular SC of the block are taken in accordance with its installation on the aircraft: the X-axis is along the longitudinal axis, the Y-axis is normal, the Z-axis is along the right wing.

Changing the rotation speed and tilt angles of the platform is set according to the program. In fig. 1 shows a programmed change in the angular velocities of the block during rotations along two axes for a set of speeds {10,50,150} [deg / s], where Row 1 - along the axes - XY, Row 2-YZ, Row 3-XZ.

The measuring axes of the DUS are directed along the axes of the oblique SC, deployed relative to the rectangular SC of the block at small angles of non-orthogonality.

To calculate the calibration coefficients, the values of the effective angular velocities along the axes of the rectangular SC of the block and the codes of the DUS signals, averaged for the time interval of steady-state rotations, are used.

Calibration of DUS on a three-axis table

Measurement models

A linear measurement model and an auxiliary nonlinear model are used to connect the DUS signals with the effective angular velocities. The linear model has the form [1]:

u = K (ω) ω + С + е, K (ω) = DS (ω), ω = ω _с + ω _g , С ^T = [с _х с _у с _z ],

Here: u is the vector of ADC codes in the oblique SC of the ADS measuring axes; ω is the vector of effective angular in the axes of the rectangular SC of the block; ω _c - vector of projections of angular velocities on the axis of the SC of the block due to the rotation of the table platform; ω _g - vector of projections of angular velocities due to the rotation of the Earth; С - vector of displacements of zeros of the DOS in code units; e - noise; K - matrix of calibration factors, taking into account the scales and angles of non-orthogonality: S - diagonal matrix of scale factors; D - matrix of angles of non-orthogonality.

, ω=ω_c, то есть угловой скоростью Земли пренебрегаем.Further it is accepted

, ω = ω _c , that is, the angular velocity of the Earth is neglected.

The linear model is used in two versions - taking into account a preliminary estimate of the vector C of displacements of zeros at a static position of the block (the model is designated as "L3"), and without it (model "L4"), when the matrix K and the vector C are determined jointly from the data of rotation processes ...

Non-linear model, designated as "NL5". It is designed to determine the change in the displacement of the zeros of the DLS depending on the values of the angular velocities acting perpendicular to the measuring axes:

u = K (ω) ω + С + е + F (ω),

where F (ω) is a vector of nonlinear functions of the form:

Taking into account a lot of experiments and for the most general case of a nonlinear model containing the largest number of coefficients, there are three systems of equations for measuring the signals of the DLS:

To analyze the effectiveness of the proposed method, three variants of the composition of the calibration coefficients determined from the rotation data are considered:

1. The linear model "L3" is identified in a known manner in two stages [1]. At the first stage, the vector C of displacements of zeros is estimated at a static position of the block. At the second stage, the matrix K is estimated, while rotations are used separately along the X, Y, Z axes. The vectors of the coefficients determined at the stage of rotations contain three elements for each SDS.

2. The linear model "L4" contains four coefficients for each DUS, determined by the results of six rotations - separately along the X, Y, Z axes, and along two XY, YZ, XZ axes. In this case, the determination of the elements of the matrix K and the vector C is performed jointly. The vectors of the coefficients of the "L4" model are as follows:

3. The nonlinear model "NL5", like the model "L4", is identified by the data of six rotations. This model contains five coefficients for each CRS. The vectors of the coefficients of the "NL5" model are as follows:

Calculation ratios for calibration factors

The vectors of measurements of the ADS signals contain the average values of the codes of the ADS signals, their dimension is equal to the number of rotations for one value of the angular velocity:

Equations for measurements of the OLS signals are presented in matrix form:

A _x a _x = B _x , A _y a _y = B _y , A _z a _z = B _z ,

where А _х , А _у , А _z - rectangular matrices, dimension (3.3) - for model "L3", dimension (4.6) - for model "L4", dimension (5.6) - for model "NL5 ".

The vector estimates of the coefficients are calculated using the least squares method:

Relationships for special software

The calculation of the current physical values of the angular velocities according to the DUS codes and calibration coefficients is performed according to the following ratios:

- для линейных моделей «L3», «L4».

- for linear models "L3", "L4".

относительно

For the nonlinear model "NL5" the nonlinear equation is solved

relatively

1. Estimating the accuracy of the original block

The mathematical expectations and root-mean-square values of the errors in estimating the angular velocities were calculated over the time interval of steady-state rotations.

From table 2, where the statistics of the reproduction of angular velocities by the original block is given, it follows that the estimates of the angular velocities formed by the original block have displacements that are hundredths [deg / s] for low angular velocities, and increase to tenths [deg / s] with an increase in the angular velocity up to 150 [deg / s]. In this case, the root-mean-square errors in the estimation of the angular velocities, caused by the measurement noise, are of the order of 0.02… 0.03 [deg / s].

2. Estimation of the tuning accuracy of the linear model "L3"

From Table 3, where the statistics of errors in the reproduction of angular velocities by the L3 model are given, it follows that almost zero displacements of the estimates of angular velocities on rotations separately along the X, Y, Z axes increase on rotations along two axes: XY, YZ, XZ. This means that the vector C, determined in the static position of the block and the matrix K, determined from the data of separate rotations along the X, Y, Z axes, are invalid for complex rotations along the two axes XY, YZ, XZ, which is especially noticeable at high angular velocities.

3. Estimation of the tuning accuracy of the linear model "L4"

From table 4, where the statistics of errors of reproduction of angular velocities by the L4 model are given, it follows that when jointly evaluating the matrix K and the vector C according to the L4 model, the errors in estimating the angular velocities are less than the errors of the original block and the errors of the L3 model, especially at low angular velocities ... An analysis of the numerical values of the coefficients shows that they undergo significant changes when the angular velocity is varied.

4. Estimation of the tuning accuracy of the nonlinear model "NL5"

From a comparison of Table 5, where the statistics of errors of reproduction of angular velocities by the NL5 model, with Table 4, it follows that the accuracy of the nonlinear model "NL5" is higher than the accuracy of the linear model "L4". At the same time, there is a good stability of the coefficients of the nonlinear model with varying angular velocity, including the coefficients b _x , b _y , b _z .

Assessment control

Next, the errors in estimating the average values of angular velocities are determined:

Here j is the experiment number.

Mathematical expectations and standard deviations of estimation errors are used for control:

The mathematical expectations of the estimation errors should be close to zero. The standard deviation of the estimation errors should be of the order of the standard deviation of the measurement noise.

The table management program includes:

- initial exhibition of the platform - for DUS "sensing" the Earth's angular velocity;

- performing a sequence of rotations and tilt angles of the platform in accordance with the 6 specified experiments with a time interval of about 3-4 minutes;

- registration of time, ADC codes, readings of three platform protractors, block temperature sensors and platform temperature sensor;

- repeating these actions for the grid of angular velocity values;

- static experiment with a stationary position of the platform for about 10 minutes.

For the full temperature range, experiments are repeated on a temperature grid

Calculated part

For one steady-state temperature value, the calculation part includes:

- selection of a time interval lasting about 2-3 minutes with a steady angular velocity and tilt angles;

- calculation of the average values of the ADC DUS codes;

- differentiation of readings of goniometers and calculation of average angular velocities of the table platform;

- calculation of average values of readings of temperature sensors;

- Calculation of calibration factors;

- control of calibration according to experiments of rotations;

- control of calibration by static experiment;

- calculation of interpolation tables by angular velocity.

For the full temperature range, the following calculations are performed:

- calibration of block temperature sensors;

- formation of interpolation tables for temperature;

- control of calibration taking into account the interpolation in terms of speed and temperature.

Technical result

According to the proposed method, the estimation of the scales and angles of non-orthogonality is performed together with the offsets of the zeros. Due to this, the invariance of the estimates of scales and angles of non-orthogonality with respect to the displacements of the zeros of the ADS is ensured, and, accordingly, an increase in accuracy, which is valuable for micromechanical DEs with a high level of instability of the displacements of zeros.

The accuracy of the non-linear model "NL5" is higher than the accuracy of the linear model "L4". At the same time, there is a good stability of the coefficients of the nonlinear model with varying angular velocity, including the coefficients b _x , b _y , b _z .

This method provides estimation of scale factors for fixed values of angular velocities. This allows it to be used to obtain a set of estimates for a set of values of angular velocities and directions of rotation for the formation of lookup tables in order to take into account the nonlinear dependences of scales on the speed and direction of rotation.

The speeds of rotation, angles of rotation of the table platform and the necessary set of experiments for accurate calculation of the calibration coefficients and ensuring the constancy and equality of the projections of the given angular velocities on the block axis are proposed.

Literature

1. Pat. US 2014372063 (A1) US, IPC7 G01P 21/00. Quick calibration method for inertial measurement unit / NIU XIAOJI [CN], etc .; applicant UNIV WUHAN [CN] - No. US 201314239145; declared 03/05/2013; publ. 12/18/2014.

2. RF No. 2269813 Method of calibrating the parameters of the strapdown inertial measuring module, / Sineev AI. and other Patentee: JSC Gazpriboravtomatikaservice, publ. 10.02.2006.

3. Volynskiy D.V., Dranitsyna E.V., Odintsov A.A., Untilov A.A. Calibration of fiber-optic gyroscopes as part of cardless inertial measurement modules. Gyroscopy and Navigation No. 2, 2012, p. 56-68.

Claims (15)

A method for improving the calibration accuracy of a block of micromechanical angular velocity sensors, including an initial platform setting, a static experiment with a stationary position of the platform, rotation using bench equipment sequentially along at least two non-parallel axes in the basis of the calibrated IDU, during rotation, the IDU readings are recorded along the linear acceleration sensor channel (DLU), the readings of the angular velocity sensors (ADS), identifying the mathematical model of the ADS, determine the zero signals of the ADS, a matrix describing the scale factors, cross-links, characterized in that a nonlinear model of micromechanical DEOS is additionally used u = K (ω) ω + С + е + F (ω), where F (ω) is a vector of nonlinear functions of the form

carry out the development of a program for automating the calibration process, which includes the execution of a sequence of rotations and tilt angles of the platform in accordance with the 6 experiments indicated below in Table 1 with a time interval of about 3-4 minutes,

processing of the obtained data, including the choice of a time interval lasting about 2-3 minutes with a steady angular velocity and tilt angles, calculating the average values of the ADC DUS codes, differentiating the readings of the goniometers and calculating the average values of the angular velocities of the table platform, there are three systems of equations for determining the calibration coefficients, each system contains six equations for measuring the DUS signals:

and for each CRS, five coefficients are determined, the vectors of which have the form:

the estimates of the vectors of the coefficients are calculated by the method of least squares, the calibration control according to the experiments of rotations is carried out by evaluating the average values of the angular velocities

mathematical expectations and standard deviations of estimation errors are used for control:

the mathematical expectations of the estimation errors must be close to zero, the standard deviation of the estimation errors must be of the order of the standard deviation of the measurement noise.

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