CN102680740A - System-level fitting calibration method for quadratic term error of accelerometer - Google Patents

Abstract

The invention discloses a system-level fitting calibration method for a quadratic term error of an accelerometer. The method comprises the eight main steps of: 1, arranging an inertia unit on a turntable, wherein the initial direction of the inertia unit is ground-east-south, and a sampling period dt is 0.01s; 2, rotating the turntable at a first position, acquiring the data of the inertia unit, and after the rotation is finished, standing the turntable for 1 minute, and stopping acquiring the data; 3, rotating the turntable at a second position, acquiring the data of the inertia unit, and after the rotation is finished, standing the turntable for 1 minute, and stopping acquiring the data; 4, rotating the turntable at a third position, namely arranging the inertia unit on the turntable in a way that the initial direction of the inertia unit is west-north-ground, acquiring the data of the inertia unit, and after the rotation is finished, standing the turntable for 1 minute, and stopping acquiring the data; 5, rotating the turntable at a fourth position, namely arranging the inertia unit on the turntable in a way that three coordinate axes face the north, the sky and the east respectively, acquiring the data of the inertia unit, and after the rotation is finished, standing the turntable for 1 minute, and stopping acquiring the data to finish the four groups of rotation; 6, performing navigation solving on each group of data acquired from the inertia unit respectively, and calculating each axial acceleration error; 7, designing a Kalman filter; and 8, performing analytical calculation to calculate the quadratic term coefficient error of the accelerometer.

Description

A kind of system-level fitting calibrating method of accelerometer quadratic term error

(1) technical field

The present invention relates to a kind of system-level fitting calibrating method of accelerometer quadratic term error, belong to the inertial navigation technology field.

(2) background technology

Calibration technique is one of the core technology in inertial navigation field; It is a kind of identification technique to error; Promptly set up the error mathematic model of inertance element and inertial navigation system, solve the error term in the error model, and then come error is compensated through software algorithm through a series of test.Demarcation can improve the precision of inertial navigation system from the software aspect, and common calibrated error item has zero error, constant multiplier error, the alignment error etc. partially of accelerometer and gyro.

Divide by level, demarcation can be divided into discrete and demarcate and system-level demarcation.The theoretical research of current discrete scaling method is comparatively ripe, and system-level scaling method is by beginning to grow up the eighties in 20th century, just becoming the focus of calibration technique research at present.

It is directly to utilize accelerometer and gyrostatic output to come its error parameter is carried out identification as observed quantity that discrete is demarcated.Discrete is demarcated the influence of with counteracting earth rotation and acceleration of gravity inertial navigation system being demarcated through the suitable rotation layout path of design.This method stated accuracy is influenced by random noise, need repeatedly test same system usually and get its mean value.

System-level demarcation is to utilize the systematic error of inertial navigation output to come the error parameter of identification inertia device as observed quantity.Compare with the discrete demarcation, the algorithm relative complex of system-level demarcation, but system-level demarcation can suppress the measurement noise in the calibration process, and shorten the nominal time, improve stated accuracy.System-level demarcation is divided into fitting calibrating again and filtering is demarcated.Fitting calibrating is through setting up special exercise excitation observation navigation error, match estimation device error parameter.Fitting calibrating method generally with navigation speed rate of change or specific force as observed quantity.Filtering is demarcated and is meant the wave filter through design Kalman, and each device error parameter of inertial navigation system as filter status, is observed each device error parameter of navigation error Filtering Estimation.

Yang Jie; Wu Wen opens " the laser gyro strapdown system high-precision accelerometer nonlinear model parameter calibration [J] " write and (sees Chinese inertial technology journal 2010; 18 (5)) proposing based on the angle positional precision is 5 " three-axle table; use the thought of least square substep identification, pick out the quadratic term error of accelerometer through quadrature six positions.This method belongs to the discrete scaling method." land is with high-precision laser gyroscope SINS error parameter Study on estimation method [D] " that Zhang Hongliang writes. Changsha: the National University of Defense technology; 2010; 10. respectively fitting calibrating method and filtering scaling method are illustrated, but do not consider the quadratic term error of accelerometer in the said scaling method of this paper.

(3) summary of the invention

1, purpose:

The purpose of this invention is to provide a kind of system-level fitting calibrating method of accelerometer quadratic term error, it has overcome the deficiency of prior art, can estimate the quadratic term error of accelerometer exactly.

2 technical schemes: the system-level fitting calibrating method of a kind of accelerometer quadratic term of the present invention error, these method concrete steps are following:

Step 1: will be used to group and be installed on the turntable, and be used to group and initially be oriented ground-east-south.Gyro output is set demarcates in advance and compensates.Be used to group energising preheating 30 minutes, sampling period dt=0.01s.

Step 2: see Fig. 1, primary importance promptly-east-south rotation.Begin to gather and be used to organize data.At first left standstill one minute, and made the angular velocity of being used to organize with 10 °/s be rotated in the forward 180 ° around the Y axle then, rotation finishes and leaves standstill one minute again, stops to adopt number.

Step 3: see Fig. 1, the second place i.e. sky-east-north rotation.Begin to gather and be used to organize data, at first make and be used to group and left standstill one minute in the step 2 rotation position that finishes, make turntable be rotated in the forward 180 ° with the angular velocity of 10 °/s around being used to organize the Z axle then, rotation finishes and leaves standstill one minute again.Stop to adopt number.

Step 4: see Fig. 1, the 3rd position is west-north-ground rotation.To be used to group and be installed on the turntable, and be used to group and initially be oriented west-north-ground.Begin to gather and be used to organize data, at first left standstill one minute, make turntable be rotated in the forward 180 ° with the angular velocity of 10 °/s around being used to organize the Y axle then, rotation finishes and leaves standstill one minute again.Stop to adopt number.

Step 5: see Fig. 1, the 4th position i.e. north-sky-east rotation.To be used to group and be installed on the turntable, three coordinate axis respectively towards north-sky-east.Begin to gather and be used to organize data, at first left standstill one minute, make turntable be rotated in the forward 180 ° with the angular velocity of 10 °/s around being used to organize the Z axle then, rotation finishes and leaves standstill one minute again.Stop to adopt number, four groups of rotations so far finish.

Step 6: the data to above each group is used to organize collection are carried out navigation calculation respectively, and calculate each axial velocity error, see Fig. 2-Fig. 5.Each group is used to organize the corresponding initial moment of data acquisition is designated as T ₀, the end of leaving standstill before the rotation one minute is designated as T constantly ₁, rotated the end of leaving standstill a minute and be designated as T constantly ₂Have only angular motion not have the line motion owing to be used to group, the system speed error can be represented with following formula:

$\mathrm{\δ}{v}_j^i\left(t\right)=v_j^i\left(t\right)$

I=1 wherein, 2,3,4, represent the rotation of i position.J=x, y, z representes the velocity error that corresponding j is axial.

Step 7: design Kalman filter.State variable does ${\left[\begin{array}{ccc}\∂v_j^i\left(t\right)& \∂{\stackrel{\·}{v}}_j^i\left(t\right)& \∂{\stackrel{\·\·}{v}}_j^i\left(t\right)\end{array}\right]}^T.$ Use standard Karman equation carries out iteration, and filtering finishes and can obtain See Fig. 6-Fig. 9.

System state equation:

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}\∂v_j^i\left(t\right)\\ \∂{\stackrel{\·}{v}}_j^i\left(t\right)\\ \∂{\stackrel{\·\·}{v}}_j^i\left(t\right)\end{array}\right]=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right]\left[\begin{array}{c}\∂v_j^i\left(t\right)\\ \∂{\stackrel{\·}{v}}_j^i\left(t\right)\\ \∂{\stackrel{\·\·}{v}}_j^i\left(t\right)\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ w_j\end{array}\right]$

Observation equation:

$Z_j=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\left[\begin{array}{c}\∂v_j^i\left(t\right)\\ \∂{\stackrel{\·}{v}}_j^i\left(t\right)\\ \∂{\stackrel{\·\·}{v}}_j^i\left(t\right)\end{array}\right]+{\mathrm{\μ}}_j$

W wherein _jAnd μ _jBe respectively state-noise and observation noise.

Step 8: analytical Calculation, obtain the quadratic term coefficient error of accelerometer.

At first order

The error observation equation is as shown in table 1 below:

Table 1 error observation equation

Then the quadratic term error is resolved as shown in table 2 below:

Table 2 quadratic term error is resolved table

Symbol description in the table is following:

What K2ax represented the x axle adds table quadratic term error, and what K2ay represented the y axle adds table quadratic term error, and what K2az represented the z axle adds table quadratic term error; K2ax K2ay K2az is the amount that this method ultimate demand is obtained; G representes acceleration of gravity, and a, b, c are the error observed quantities of finding the solution in the K2a process, can analytical Calculation go out K2a through a, b, c, and the method for asking in detail of a, b, c is seen upward table 1.

3, advantage and effect:

The invention has the advantages that: 1, can calibrate the quadratic term coefficient error of accelerometer exactly, effectively improve the service precision of accelerometer based on system-level fitting process; 2, demarcate the path and only need four rotations, simplified operating process.

(4) description of drawings:

The detailed rotate path synoptic diagram of this scaling method of Fig. 1

Fig. 2 primary importance rotary course is used to organize the navigation speed error of X, Y, three axles of Z

Fig. 3 second place rotary course is used to organize the navigation speed error of X, Y, three axles of Z

Fig. 4 the 3rd position rotary course is used to organize X, Y, three spindle guide speed of a ship or plane of Z degree error

Fig. 5 the 4th position rotary course is used to organize X, Y, three spindle guide speed of a ship or plane of Z degree error

Fig. 6 primary importance rotary course is used to organize the estimated value of X, Y, three axle velocity errors of Z rate of change

Fig. 7 second place rotary course is used to organize the estimated value of X, Y, three axle velocity errors of Z rate of change

Fig. 8 the 3rd position rotary course is used to organize the estimated value of X, Y, three axle velocity errors of Z rate of change

Fig. 9 the 4th position rotary course is used to organize the estimated value of X, Y, three axle velocity errors of Z rate of change

Figure 10 FB(flow block) of the present invention

Symbol description is following among the figure:

E, S, W, N, U, D represent towards east respectively, south, west, north, heaven and earth

(5) embodiment:

See Figure 10, the system-level fitting calibrating method of a kind of accelerometer quadratic term of the present invention error, these method concrete steps are following:

Step 1: will be used to group and be installed on the turntable, and be used to group and initially be oriented ground-Dong-Nan.Supposing to put gyro output demarcates in advance and compensates.Be used to group energising preheating 30 minutes, sampling period dt=0.01s.

Step 2: primary importance promptly-Dong-Nan rotation.Begin to gather and be used to organize data.At first left standstill one minute, and made the angular velocity of being used to organize with 10 °/s be rotated in the forward 180 ° around the Y axle then, rotation finishes and leaves standstill one minute again, stops to adopt number.See Fig. 1.

Step 3: the second place i.e. sky-Dong-north rotation.Begin to gather and be used to organize data, at first make and be used to group and left standstill one minute in the step 2 rotation position that finishes, make turntable be rotated in the forward 180 ° with the angular velocity of 10 °/s around being used to organize the Z axle then, rotation finishes and leaves standstill one minute again.Stop to adopt number.See Fig. 1.

Step 4: the 3rd position is west-north-ground rotation.To be used to group and be installed on the turntable, and be used to group and initially be oriented west-north-ground.Begin to gather and be used to organize data, at first left standstill one minute, make turntable be rotated in the forward 180 ° with the angular velocity of 10 °/s around being used to organize the Y axle then, rotation finishes and leaves standstill one minute again.Stop to adopt number.See Fig. 1.

Step 5: the 4th position i.e. north-sky-Dong rotation.To be used to group and be installed on the turntable, three coordinate axis respectively towards north-sky-Dong.Begin to gather and be used to organize data, at first left standstill one minute, make turntable be rotated in the forward 180 ° with the angular velocity of 10 °/s around being used to organize the Z axle then, rotation finishes and leaves standstill one minute again.Stop to adopt number, four groups of rotations so far finish.See Fig. 1.

Step 6: see Fig. 2-Fig. 5, the data that above each group is used to organize collection are carried out navigation calculation respectively, and the computing velocity error.Each group is used to organize the corresponding initial moment of data acquisition is designated as T ₀, the end of leaving standstill before the rotation one minute is designated as T constantly ₁, rotated the end of leaving standstill a minute and be designated as T constantly ₂Have only angular motion not have the line motion owing to be used to group, the system speed error can be represented with following formula:

$\mathrm{\δ}{v}_j^i\left(t\right)=v_j^i\left(t\right)$

I=1 wherein, 2,3,4, represent the rotation of i position.J=x, y, z representes the velocity error that corresponding j is axial.

Step 7: design Kalman filter.State variable does ${\left[\begin{array}{ccc}\∂v_j^i\left(t\right)& \∂{\stackrel{\·}{v}}_j^i\left(t\right)& \∂{\stackrel{\·\·}{v}}_j^i\left(t\right)\end{array}\right]}^T.$ Use standard Karman equation carries out iteration, and filtering finishes and can obtain

See Fig. 6-Fig. 9.

System state equation:

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}\∂v_j^i\left(t\right)\\ \∂{\stackrel{\·}{v}}_j^i\left(t\right)\\ \∂{\stackrel{\·\·}{v}}_j^i\left(t\right)\end{array}\right]=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right]\left[\begin{array}{c}\∂v_j^i\left(t\right)\\ \∂{\stackrel{\·}{v}}_j^i\left(t\right)\\ \∂{\stackrel{\·\·}{v}}_j^i\left(t\right)\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ w_j\end{array}\right]$

Observation equation:

$Z_j=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\left[\begin{array}{c}\∂v_j^i\left(t\right)\\ \∂{\stackrel{\·}{v}}_j^i\left(t\right)\\ \∂{\stackrel{\·\·}{v}}_j^i\left(t\right)\end{array}\right]+{\mathrm{\μ}}_j$

W wherein _jAnd μ _jBe respectively state-noise and observation noise.

Step 8: analytical Calculation, obtain the quadratic term coefficient error of accelerometer.

At first order

The error observation equation is as shown in table 1 below:

Table 1 error observation equation

Then the quadratic term error is resolved as shown in table 2 below:

Table 2 quadratic term error is resolved table

The emulation exemplifying embodiment

1. group output is used in simulation.Emulation device error source is seen table 3.The rotation layout is as shown in table 4 below:

Table 3 emulation device error source

Table 4 emulation rotation layout sequence

Position of rotation	Initially towards	Initial angle	Rotation axis/turn to
				Primary importance	Ground-Dong-Nan	[0,90,-90]	Y/ just changes
The second place	My god-Dong-north	[0,-90,-90]	Z/ just changes
				The 3rd position	West-north-ground	[0,180,0]	Y/ just changes
The 4th position	North-sky-Dong	[90,0，90]	Z/ just changes

It is following that accelerometer is demarcated used error model:

$\left[\begin{array}{c}\mathrm{\&delta;}{f}_x^b\\ \mathrm{\&delta;}{f}_y^b\\ \mathrm{\&delta;}{f}_z^b\end{array}\right]=\left[\begin{array}{ccc}{K}_{a1x}& {\mathrm{aMA}}_{\mathrm{xy}}& {\mathrm{aMA}}_{\mathrm{xz}}\\ {\mathrm{aMA}}_{\mathrm{yx}}& K_{a1y}& {\mathrm{aMA}}_{\mathrm{yz}}\\ {\mathrm{aMA}}_{\mathrm{zx}}& {\mathrm{aMA}}_{\mathrm{zy}}& K_{a1z}\end{array}\right]\left[\begin{array}{c}{f}_x^b\\ f_y^b\\ f_z^b\end{array}\right]+\left[\begin{array}{ccc}{K}_{a2x}& K_{a2\mathrm{xy}}& K_{a2\mathrm{xz}}\\ K_{a2\mathrm{yx}}& K_{a2y}& K_{a2\mathrm{yz}}\\ K_{a2\mathrm{zx}}& K_{a2\mathrm{zy}}& K_{a2z}\end{array}\right]{\left[\begin{array}{c}{f}_x^b\\ f_y^b\\ {\mathrm{<figure-callout\; id="2"\; label="f\; z\; b"\; filenames="HDA00001611723500022.png"\; state="\{\{state\}\}">f</figure-callout>}}_{zb}^{}\end{array}\right]}^2+\left[\begin{array}{c}{B}_{\mathrm{ax}}\\ B_{\mathrm{ay}}\\ B_{\mathrm{az}}\end{array}\right]$

B wherein _AjRepresent the partially zero of j axis accelerometer, K _1ajThe constant multiplier error of expression j axis accelerometer, K _A2jThe quadratic term error of expression j axis accelerometer, aMA representes the alignment error of accelerometer, K _A2ijThe cross-couplings item of expression accelerometer.f ^bBe the ideal output of accelerometer, δ f ^bBe the error output of accelerometer.

2. utilize contain phantom error be used to organize data and carry out navigation calculation.

3. the result with navigation calculation carries out Kalman filtering, and the wave filter basic parameter is set according to step 7 in the technical scheme.If state variable initial value

System noise acoustic matrix initial value W=[0,0,1e ^-2] ^T, observation noise battle array R=1e ^-2Filtering obtains

4. according to step 8 in the technical scheme, calculate the quadratic term coefficient error of accelerometer, and compare with emulation error originated from input source.Accelerometer quadratic term error calibration is the result see shown in the table 5:

Table 5 accelerometer quadratic term error calibration is the deck watch as a result

Simulation result shows that this scaling method is correctly feasible, can satisfy the demarcation demand of accelerometer quadratic term error.

Claims (1)

1. the system-level fitting calibrating method of an accelerometer quadratic term error, it is characterized in that: these method concrete steps are following:

Step 1: will be used to group and be installed on the turntable, and be used to group and initially be oriented ground-east-south; Gyro output is set demarcates in advance and compensate, be used to group energising preheating 30 minutes, sampling period dt=0.01s;

Step 2: primary importance promptly-east-south rotation, begin to gather and be used to organize data, at first left standstill one minute, make then and be used to group and be rotated in the forward 180 ° around the Y axle with the angular velocity of 10 °/s, rotation finishes and leaves standstill one minute again, stops to adopt number;

Step 3: the second place i.e. sky-east-north rotation; Begin to gather and be used to organize data, at first make and be used to group and left standstill one minute, make turntable be rotated in the forward 180 ° around being used to organize the Z axle then with the angular velocity of 10 °/s in the step 2 rotation position that finishes; Rotation finishes and leaves standstill one minute again, stops to adopt number;

Step 4: the 3rd position is west-north-ground rotation, begins to gather and is used to organize data, at first leaves standstill one minute, makes turntable be rotated in the forward 180 ° with the angular velocity of 10 °/s around being used to organize the Y axle then, and rotation finishes and leaves standstill one minute again, stops to adopt number;

Step 5: the 4th position i.e. north-sky-east rotation, begins to gather and is used to organize data, at first leaves standstill one minute; Make turntable be rotated in the forward 180 ° around being used to organize the Z axle then with the angular velocity of 10 °/s; Rotation finishes and leaves standstill one minute again, stops to adopt number, and four groups of rotations so far finish;

Step 6: the data to above each group is used to organize collection are carried out navigation calculation respectively, and calculate each axial velocity error, each group is used to organize the corresponding initial moment of data acquisition is designated as T ₀, the end of leaving standstill before the rotation one minute is designated as T constantly ₁, rotated the end of leaving standstill a minute and be designated as T constantly ₂Have only angular motion not have the line motion owing to be used to group, the system speed error is represented with following formula:

$\mathrm{\&delta;}{v}_j^i\left(t\right)=v_j^i\left(t\right)$

I=1 wherein, 2,3,4, represent the rotation of i position; J=x, y, z representes the velocity error that corresponding j is axial;

Step 7: design Kalman filter; State variable does ${\left[\begin{array}{ccc}\&PartialD;v_j^i\left(t\right)& \&PartialD;{\stackrel{\&CenterDot;}{v}}_j^i\left(t\right)& \&PartialD;{\stackrel{\&CenterDot;\&CenterDot;}{v}}_j^i\left(t\right)\end{array}\right]}^T;$ Use standard Karman equation carries out iteration, and filtering finishes and obtains

System state equation:

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}\&PartialD;v_j^i\left(t\right)\\ \&PartialD;{\stackrel{\&CenterDot;}{v}}_j^i\left(t\right)\\ \&PartialD;{\stackrel{\&CenterDot;\&CenterDot;}{v}}_j^i\left(t\right)\end{array}\right]=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right]\left[\begin{array}{c}\&PartialD;v_j^i\left(t\right)\\ \&PartialD;{\stackrel{\&CenterDot;}{v}}_j^i\left(t\right)\\ \&PartialD;{\stackrel{\&CenterDot;\&CenterDot;}{v}}_j^i\left(t\right)\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ w_j\end{array}\right]$

Observation equation:

$Z_j=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\left[\begin{array}{c}\&PartialD;v_j^i\left(t\right)\\ \&PartialD;{\stackrel{\&CenterDot;}{v}}_j^i\left(t\right)\\ \&PartialD;{\stackrel{\&CenterDot;\&CenterDot;}{v}}_j^i\left(t\right)\end{array}\right]+{\mathrm{\&mu;}}_j$

W wherein _jAnd μ _jBe respectively state-noise and observation noise;

Step 8: analytical Calculation, obtain the quadratic term coefficient error of accelerometer;

At first order

The error observation equation is as shown in table 1 below:

Table 1 error observation equation

Then the quadratic term error is resolved as shown in table 2 below:

Table 2 quadratic term error is resolved table

Symbol description in the table is following:

What K2ax represented the x axle adds table quadratic term error, and what K2ay represented the y axle adds table quadratic term error, and what K2az represented the z axle adds table quadratic term error; K2ax K2ay K2az is the amount that ultimate demand is obtained; G representes acceleration of gravity, and a, b, c are the error observed quantities of finding the solution in the K2a process, go out K2a through a, b, c analytical Calculation, and the method for asking in detail of a, b, c is seen upward table 1.

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