CN101907638B - Method for calibrating accelerometer under unsupported state - Google Patents

Abstract

The invention discloses a method for calibrating an accelerometer under an unsupported state, which is applied to an inertial navigation system with the capacity of initially aligning with a static base attitude. The method comprises the following steps of: firstly, simplifying an error model, repeatedly changing the carrier position, and coarsely and finely aligning with each position by using the static base to acquire the attitude information; and calculating the three-axis component of an acceleration of gravity g projected under a carrier coordinate system according to the attitude information, and recording the measured value of the accelerometer at each position. The invention provides a 10-position calibrating scheme, which comprises the following steps of: acquiring zero offset to degenerate the error model into a linear model by identifying the zero offset through a nonlinear least square method according to the calculated value and measured value of the projected component; and mounting an error and scale factor coupled matrix by identifying through a linear least square method. Therefore, the key parameters of the accelerometer are calibrated. The method has the advantages of capacities of realizing unsupported calibration of the accelerometer and effectively estimating the key parameters of the accelerometer with time-varying performance, along with simple process and high speed.

Description

A kind of scaling method of accelerometer under unsupported state

Technical field

The invention belongs to the inertial navigation technology field, be specifically related to a kind of scaling method of accelerometer under unsupported state.

Background technology

Accelerometer is effectively demarcated the problem that can solve its performance parameter time variation, very necessary to improving measuring accuracy.Traditional scaling method need carry out complete system-level demarcation to unknown parameter by calibration facilities such as turntable, hydro-extractors, stated accuracy height, but complicated operation, and the demarcation cycle is long, and real-time is relatively poor; So proposed the notion that accelerometer under unsupported state is demarcated at the problems referred to above, promptly require to break away from laboratory condition, only by inertia device self, can realize demarcating at the use scene, because the restriction on the on-site proving condition, usually only carry out identification at the most serious parameter of accelerometer performance impact, it is also fewer that the accelerometer of publishing does not at present have the on-site proving of support document.

Still prompt, the Gu Qitai of Tsing-Hua University's exact instrument and Mechanical Academy propose the on-the-spot optimal calibration method based on virtual noise, promptly two go on foot the estimations technique, this method with the multiposition method relatively, has advantage simple in structure, that save time, be easy to realize, but can not calibrate alignment error and scale factor error, and only be applicable to short time, low middle precision navigational system.

The Liu Baiqi of BJ University of Aeronautics ﹠ Astronautics, room build up at optical fibre gyro IMU and propose six positions rotation field calibration method, on six positions, carry out the rotation of ten secondaries by surface level, set up 42 non-linear input and output equations, disappear mutually with the symmetric position error by the rotation integration, carry out the inertia device parameter calibration, this method operation is complicated, and whether level has high requirement to Plane of rotation, and can not pick out the alignment error and the scale factor error of accelerometer.

W T Fong, the S K Ong of NUS and A Y C Nee propose a kind of based on the optimized identification scheme of downhill simple, simple to operate, and can pick out complete error parameter, the document is primarily aimed at micromechanics IMU design, be subjected to the restriction of device measuring accuracy, error model is simplified serious, and the identification result precision is lower.

Summary of the invention

In order to solve the above-mentioned alignment error and the scale factor error that can not mark or discern accelerometer, the problem that the identification result precision is low, the present invention proposes a kind of scaling method of accelerometer under unsupported state, need at first before carrying out calibration process to consider that to the most serious error parameter of accelerometer performance impact the error model of simplifying three axis accelerometer is

$\left(\begin{array}{c}{g}_{\mathrm{xa}}\\ g_{\mathrm{ya}}\\ g_{\mathrm{za}}\end{array}\right)=\left(\begin{array}{ccc}{K}_{11}{k}_x& K_{12}{k}_y& K_{13}{k}_z\\ K_{21}{k}_x& K_{22}{k}_y& K_{23}{k}_z\\ K_{31}{k}_x& K_{32}{k}_y& K_{33}{K}_z\end{array}\right)\left(\begin{array}{c}(g_{\mathrm{xm}}-g_{x0})\\ (g_{\mathrm{ym}}-g_{y0})\\ (g_{\mathrm{zm}}-g_{z0})\end{array}\right)---\left(1\right)$

In the formula, k _x, k _y, k _zBe accelerometer x, y, z axle scale factor; K ₁₁, K ₁₂, K ₁₃, K ₂₁, K ₂₂, K ₂₃, K ₃₁, K ₃₂, K ₃₃Be the alignment error matrix element; g _X0, g _Y0, g _Z0Be accelerometer x, y, z axle zero drift; g _Xm, g _Ym, g _ZmBe accelerometer x, y, z axle measured value; g _Xa, g _Ya, g _ZaBe gravity acceleration g projection components under carrier coordinate system;

Coupled matrix for alignment error and scale factor.

And then finish demarcation by 5 steps:

Step 1: quiet pedestal coarse alignment obtains carrier roll angle γ, pitching angle theta;

Step 2: utilize Kalman filtering to carry out quiet pedestal fine alignment, improve the alignment precision of roll angle γ, pitching angle theta, and further obtain the calculated value (g of three components of the projection of gravity acceleration g under carrier coordinate system _Xa, g _Ya, g _Za);

Step 3: carrier is carried out step 1, step 2 acquisition 10 groups of accelerometer x, y, z axle measured value (g on 10 different positions _Xm, g _Ym, g _Zm) and the calculated value (g of three components of 10 groups of gravity acceleration g projections under carrier coordinate system _Xa, g _Ya, g _Za).Whether on 10 positions, place to finish according to carrier in this step and judge and carry out, do not finish, then change step 1 and carry out,, then obtain desired data, continue step 4 if finish if place.

Step 4: the zero drift g that obtains accelerometer by nonlinear least square method _X0, g _Y0, g _Z0

Step 5: obtain coupled matrix by linear least square

Step 4 is obtained zero drift g _X0, g _Y0, g _Z0And in the step 5 in the value substitution formula (1) of coupled matrix, structure formula (1) error model.Thereby can be to the measured value g of accelerometer _Xm, g _Ym, g _Zm, effectively revise, obtain revised gravity acceleration g projection components g under carrier coordinate system _Xa, g _Ya, g _ZaThereby, improved the precision of measuring.

The invention has the advantages that:

(1) nothing that can realize accelerometer under the condition of external field is relied on demarcation, breaks away from laboratory condition, not by means of traditional calibration facility;

(2) calibration process is simple, and demarcation speed is fast, can realize all demarcating before the each use of accelerometer, has effectively solved the problem of performance parameter time variation.

(3) application of non-linear least square method can solve the nonlinear problem of error model, has avoided the dependence of traditional demarcation to calibration facilities such as turntables, has realized the demarcation under the accelerometer unsupported state.

Description of drawings

Fig. 1 is the flow chart of steps of scaling method of the present invention.

Embodiment

Below in conjunction with accompanying drawing the present invention is further described in detail.

Before demarcating, the present invention needs at first to simplify the error model of three axis accelerometer:

Under the prerequisite of Biao Dinging, only consider the most serious error parameter of accelerometer performance impact can be reduced to the error model of three axis accelerometer at the scene:

$\left(\begin{array}{c}{g}_{\mathrm{xa}}\\ g_{\mathrm{ya}}\\ g_{\mathrm{za}}\end{array}\right)=\left(\begin{array}{ccc}{K}_{11}& K_{12}& K_{13}\\ K_{21}& K_{22}& K_{23}\\ K_{31}& K_{32}& K_{33}\end{array}\right)\left(\begin{array}{c}{k}_x(g_{\mathrm{xm}}-g_{x0})\\ k_y(g_{\mathrm{ym}}-g_{y0})\\ k_z(g_{\mathrm{zm}}-g_{z0})\end{array}\right)---\left(1\right)$

In the formula,

Be alignment error matrix, K ₁₁, K ₁₂, K ₁₃, K ₂₁, K ₂₂, K ₂₃, K ₃₁, K ₃₂And K ₃₃Be the alignment error matrix element; k _x, k _y, k _zBe accelerometer x, y, z axle scale factor; g _X0, g _Y0, g _Z0Be accelerometer x, y, z axle zero drift; g _Xm, g _Ym, g _ZmBe accelerometer x, y, z axle measured value; g _Xa, g _Ya, g _ZaCalculated value for gravity acceleration g projection components under carrier coordinate system.

The further abbreviation of formula (1) is merged and can get:

$\left(\begin{array}{c}{g}_{\mathrm{xa}}\\ g_{\mathrm{ya}}\\ g_{\mathrm{za}}\end{array}\right)=\left(\begin{array}{ccc}{K}_{11}{k}_x& K_{12}{k}_y& K_{13}{k}_z\\ K_{21}{k}_x& K_{22}{k}_y& K_{23}{k}_z\\ K_{31}{k}_x& K_{32}{k}_y& K_{33}{K}_z\end{array}\right)\left(\begin{array}{c}(g_{\mathrm{xm}}-g_{x0})\\ (g_{\mathrm{ym}}-g_{y0})\\ (g_{\mathrm{zm}}-g_{z0})\end{array}\right)---\left(2\right)$

Wherein,

Coupled matrix S for alignment error and scale factor.

The simplified way that the coupled matrix S of alignment error and scale factor is expressed as:

$S=\left(\begin{array}{ccc}{S}_{11}& S_{12}& S_{13}\\ S_{21}& S_{22}& S_{23}\\ S_{31}& S_{32}& S_{33}\end{array}\right)---\left(3\right)$

Wherein, shown in the formula (3) in the matrix in element and the formula (2) in the coupled matrix of alignment error and scale factor element corresponding one by one;

The scaling method of a kind of accelerometer under unsupported state of the present invention, by following 5 the step accelerometer is demarcated, concrete steps are as follows:

Step 1: quiet pedestal coarse alignment obtains carrier roll angle γ, pitching angle theta.Alignment error with carrier roll angle γ, pitching angle theta in the embodiment of the invention is controlled in 1 °, specifically obtains carrier roll angle γ, pitching angle theta realizes by following process.

By:

$\left(\begin{array}{c}{g}_x^b\\ g_y^b\\ g_z^b\end{array}\right)=C_n^b\left(\begin{array}{c}{g}_x^n\\ g_y^n\\ g_z^n\end{array}\right)---\left(4\right)$

$\left(\begin{array}{c}{\mathrm{\ω}}_{\mathrm{iex}}^b\\ {\mathrm{\ω}}_{\mathrm{iey}}^b\\ {\mathrm{\ω}}_{\mathrm{iez}}^b\end{array}\right)=C_n^b\left(\begin{array}{c}{\mathrm{\ω}}_{\mathrm{iex}}^n\\ {\mathrm{\ω}}_{\mathrm{iey}}^n\\ {\mathrm{\ω}}_{\mathrm{iez}}^n\end{array}\right)---\left(5\right)$

Obtain the carrier coordinate system of carrier and the direction cosine matrix between the geographic coordinate system:

$C_n^b=\left[\begin{array}{ccc}{g}_x^b& {\mathrm{\ω}}_{\mathrm{iex}}^b& {\mathrm{\ω}}_{\mathrm{iez}}^b{g}_y^b-{\mathrm{\ω}}_{\mathrm{iey}}^b{g}_z^b\\ g_y^b& {\mathrm{\ω}}_{\mathrm{iey}}^b& {\mathrm{\ω}}_{\mathrm{iex}}^b{g}_z^b-{\mathrm{\ω}}_{\mathrm{iez}}^b{g}_x^b\\ g_z^b& {\mathrm{\ω}}_{\mathrm{iez}}^b& {\mathrm{\ω}}_{\mathrm{iez}}^b{g}_x^b-{\mathrm{\ω}}_{\mathrm{iex}}^b{g}_y^b\end{array}\right]\·\left[\begin{array}{ccc}0& \frac{1}{g}\tan L& -\frac{1}{g}\\ 0& \frac{1}{{\mathrm{\ω}}_{\mathrm{ie}}}\sec L& 0\\ \frac{1}{{\mathrm{g\ω}}_{\mathrm{ie}}}\sec L& 0& 0\end{array}\right]$

$=\left[\begin{array}{ccc}({\mathrm{\ω}}_{\mathrm{iez}}^b{g}_y^b-{\mathrm{\ω}}_{\mathrm{iey}}^b{g}_z^b)\·\frac{1}{g{\mathrm{\ω}}_{\mathrm{ie}}}\sec L& g_x^b\·\frac{1}{g}\tan L+{\mathrm{\ω}}_{\mathrm{iex}}^b\·\frac{1}{{\mathrm{\ω}}_{\mathrm{ie}}}\sec L& -g_x^b\·\frac{1}{g}\\ ({\mathrm{\ω}}_{\mathrm{iex}}^b{g}_z^b-{\mathrm{\ω}}_{\mathrm{iez}}^b{g}_x^b)\·\frac{1}{g{\mathrm{\ω}}_{\mathrm{ie}}}\sec l& g_y^b\·\frac{1}{g}\tan L+{\mathrm{\ω}}_{\mathrm{iey}}^b\·\frac{1}{{\mathrm{\ω}}_{\mathrm{ie}}}\sec L& -g_y^b\·\frac{1}{g}\\ ({\mathrm{\ω}}_{\mathrm{iey}}^b{g}_x^b-{\mathrm{\ω}}_{\mathrm{iex}}^b{g}_y^b)\·\frac{1}{{\mathrm{g\ω}}_{\mathrm{ie}}}\sec L& g_z^b\·\frac{1}{g}\tan L+{\mathrm{\ω}}_{\mathrm{iez}}^b\·\frac{1}{{\mathrm{\ω}}_{\mathrm{ie}}}\sec L& -g_z^b\·\frac{1}{g}\end{array}\right]---\left(6\right)$

Wherein,

Three component measurement values for gravity acceleration g projection under carrier coordinate system;

Three components for gravity acceleration g projection under geographic coordinate system; ω _IeBeing rotational-angular velocity of the earth, is a constant, and numerical value is 7.292115147e-5 radian per second;

Be the three spool components of rotational-angular velocity of the earth in the carrier coordinate system projection;

Three components for rotational-angular velocity of the earth projection under Department of Geography; L is local geographic latitude; G is a local gravitational acceleration.

The simplified way that direction cosine matrix in the formula (6) is expressed as:

$C_n^b=\left[\begin{array}{ccc}{T}_{11}& T_{12}& T_{13}\\ T_{21}& T_{22}& T_{23}\\ T_{31}& T_{32}& T_{33}\end{array}\right]---\left(7\right)$

Wherein, shown in the formula (7) in the matrix in element and formula (6) matrix element corresponding one by one;

Thus, according to formula (7) can obtain the carrier error at 1 ° with interior pitching angle theta, roll angle γ:

θ＝sin ^-1T ₂₃ (8)

γ＝tg ^-1(-T ₁₃/T ₃₃) (9)

Step 2: utilize Kalman filtering to carry out quiet pedestal fine alignment, improve the alignment precision of roll angle γ, pitching angle theta, obtain pitching angle theta ', roll angle γ '.

In the embodiment of the invention with the carrier alignment error in 50 rads, specifically obtain pitching angle theta ', the process of roll angle γ ' is as follows.

Kalman filtering is applied in the quiet pedestal fine alignment, and Kalman filter state equation is:

$\left(\begin{array}{c}{\stackrel{\·}{\mathrm{\φ}}}_x\\ {\stackrel{\·}{\mathrm{\φ}}}_y\\ {\stackrel{\·}{\mathrm{\φ}}}_z\\ {\stackrel{\·}{\mathrm{\ϵ}}}_x\\ {\stackrel{\·}{\mathrm{\ϵ}}}_y\\ {\stackrel{\·}{\mathrm{\ϵ}}}_z\\ {\stackrel{\·}{\▿}}_x\\ {\stackrel{\·}{\▿}}_y\\ \stackrel{\·}{\mathrm{\δ}}{V}_x\\ \stackrel{\·}{\mathrm{\δ}}{V}_y\end{array}\right)=\left(\begin{array}{cccccccccc}0& {\mathrm{\ω}}_{\mathrm{ie}}\sin L& -{\mathrm{\ω}}_{\mathrm{ie}}\cos L& 1& 0& 0& 0& 0& 0& -1/R\\ -{\mathrm{\ω}}_{\mathrm{ie}}\sin L& 0& 0& 0& 1& 0& 0& 0& 1/R& 0\\ {\mathrm{\ω}}_{\mathrm{ie}}\cos L& 0& 0& 0& 0& 1& 0& 0& \mathrm{tgL}/R& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& -g& 0& 0& 0& 0& 0& 0& 0& 0\\ g& 0& 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right)\left(\begin{array}{c}{\mathrm{\φ}}_x\\ {\mathrm{\φ}}_y\\ {\mathrm{\φ}}_z\\ {\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\ϵ}}_z\\ {\▿}_x\\ {\▿}_y\\ \mathrm{\δ}{V}_x\\ \mathrm{\δ}{V}_y\end{array}\right)---\left(10\right)$

Equation is measured in Kalman filtering:

$\left(\begin{array}{c}\mathrm{\δ}{V}_x\\ \mathrm{\δ}{V}_y\end{array}\right)=\left(\begin{array}{cccccccccc}0& 0& 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right)\left(\begin{array}{c}{\mathrm{\φ}}_x\\ {\mathrm{\φ}}_y\\ {\mathrm{\φ}}_z\\ {\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\ϵ}}_z\\ {\▿}_x\\ {\▿}_y\\ \mathrm{\δ}{V}_x\\ \mathrm{\δ}{V}_y\end{array}\right)+\left(\begin{array}{c}{\mathrm{\η}}_x\\ {\mathrm{\η}}_y\end{array}\right)---\left(11\right)$

Wherein, φ _x, φ _y, φ _zBe respectively carrier pitch error angle, roll error angle, course error angle; ε _x, ε _y, ε _zBe respectively carrier coordinate system x, the axial gyro error of y, z are installed;

Be respectively carrier coordinate system x, y axial acceleration meter error are installed; δ V _x, δ V _yBe respectively carrier coordinate system x, the axial bearer rate error of y are installed; R is an earth radius; η _x, η _yBe respectively carrier coordinate system x, y axle speed noise are installed; L is local geographic latitude.

Through type (10), formula (11) can obtain φ _x, φ _y, φ _z, ε _x, ε _y, ε _z,

δ V _x, δ V _y

By φ _x, φ _y, φ _zForm error matrix, making it is C, is expressed as follows:

$C=\left[\begin{array}{ccc}1& -{\mathrm{\φ}}_z& -{\mathrm{\φ}}_y\\ {\mathrm{\φ}}_z& 1& {\mathrm{\φ}}_x\\ {\mathrm{\φ}}_y& -{\mathrm{\φ}}_x& 1\end{array}\right]---\left(12\right)$

Then can get the direction cosine matrix behind the fine alignment

$C_n^{\′b}=C_n^b*C=\left[\begin{array}{ccc}{T}_{11}+T_{12}*{\mathrm{\φ}}_z+T_{13}*{\mathrm{\φ}}_y& -T_{11}*{\mathrm{\φ}}_z+T_{12}-T_{13}*{\mathrm{\φ}}_x& -T_{11}*{\mathrm{\φ}}_y+T_{12}*{\mathrm{\φ}}_x+T_{13}\\ T_{21}+T_{22}*{\mathrm{\φ}}_z+T_{23}*{\mathrm{\φ}}_y& -T_{21}*{\mathrm{\φ}}_z+T_{22}-T_{23}*{\mathrm{\φ}}_x& -T_{21}*{\mathrm{\φ}}_y+T_{22}*{\mathrm{\φ}}_x+T_{23}\\ T_{31}+T_{32}*{\mathrm{\φ}}_z+T_{33}*{\mathrm{\φ}}_y& -T_{31}*{\mathrm{\φ}}_z+T_{32}-T_{33}*{\mathrm{\φ}}_x& -T_{31}*{\mathrm{\φ}}_y+T_{32}*{\mathrm{\φ}}_x+T_{33}\end{array}\right]---\left(13\right)$

With the direction cosine matrix behind the fine alignment

The simplified way that is expressed as:

$C_n^{\′b}=\left[\begin{array}{ccc}{T}_{11}^{\′}& T_{12}^{\′}& T_{13}^{\′}\\ T_{21}^{\′}& T_{22}^{\′}& T_{23}^{\′}\\ T_{31}^{\′}& T_{32}^{\′}& T_{33}^{\′}\end{array}\right]---\left(14\right)$

Wherein, the direction cosine matrix behind element and formula (13) fine alignment in the matrix shown in the formula (14)

Middle element is corresponding one by one.Through type (14) can get:

θ′＝sin ^-1T′ ₂₃ (15)

γ′＝tg ^-1(-T′ ₁₃/T′ ₃₃) (16)

Thereby obtain the carrier alignment error 50 rads with interior pitching angle theta ', roll angle γ '.Gravity acceleration g is projected under the carrier coordinate system, can obtain the calculated value of three components of the projection of gravity acceleration g under carrier coordinate system:

g _xa＝-sin(γ′)·cos(θ′)·g (17)

g _ya＝sin(θ′)·g (18)

g _za＝cos(γ′)·cos(θ′)·g (19)

Step 3: carrier is placed 10 different positions, on each position, all need to carry out quiet pedestal coarse alignment and quiet pedestal fine alignment in step 1 and the step 2, judge whether 10 positions place and finish, then do not change step 1 and carry out if finish, if finish, then obtain 10 groups of accelerometer x, y, z axle measured value (g _Xm, g _Ym, g _Zm) and the calculated value (g of three components of 10 groups of gravity acceleration g projections under carrier coordinate system _Xa, g _Ya, g _Za).

Step 4: the zero drift g that obtains accelerometer by nonlinear least square method _X0, g _Y0, g _Z0

A, establishing target function;

Formula (2) distortion can be made objective function according to formula (3)

f(p)＝[S ₁₁(g _xm-g _x0)+S ₁₂(g _ym-g _y0)+S ₁₃(g _zm-g _z0)] ²+[S ₂₁(g _xm-g _x0)+S ₂₂(g _ym-g _y0)+S ₂₃(g _zm-g _z0)] ² (20)

+[S ₃₁(g _xm-g _x0)+S ₃₂(g _ym-g _y0)+S ₃₃(g _zm-g _z0)] ²-(g _xp ²+g _yp ²+g _zp ²)

Wherein, p=[g _X0, g _Y0, g _Z0, S ₁₁, S ₁₂, S ₁₃, S ₂₁, S ₂₂, S ₂₃, S ₃₁, S ₃₂, S ₃₃];

B, ask the Jacobi matrix of objective function f (p);

The Jacobi matrix J of objective function f (p) is:

In the formula, f ₁... f ₁₀Be the objective function f (p) under the 1st to the 10th position; p ₁... p ₁₂The the 1st to the 12nd element for vectorial p.

C, iterative approach unknown vector p;

Solve an equation:

$(J_k^T{J}_k+v_{k}I){\mathrm{\δ}}^{\left(k\right)}=-J_k^T{f}^{\left(k\right)}---\left(22\right)$

Obtain vectorial p k step correction δ ^(k)

Wherein, J _kBe Jacobi matrix J k step updating value,

Be J _kTransposition; v _kBe adjustable iteration step length; I is 12 rank unit matrix;

Be objective function f (p) the renewal result in k step when the 1st to the 10th position;

By

p ^(k+1)＝p ^(k)+δ ^(k) (23)

In the formula, p ^(k+1)For p goes on foot updating value to flow control k+1; p ^(k)For p goes on foot updating value to flow control k; To formula (20), (21), (22), (23) find the solution iteration repeatedly, converge to stationary value up to vectorial p.First three element g of vector p _X0, g _Y0, g _Z0Be the zero drift of accelerometer.

Step 5: obtain coupled matrix S by linear least square;

With the zero drift g that obtains in the step 4 _X0, g _Y0, g _Z0Bring formula (2) into, formula (2) error model can be degenerated into linearity, utilize linear least square can try to achieve coupled matrix S to be:

S＝(R*(G ^T*(G*G ^T) ^-1)) ^-1 (25)

Wherein:

$G=\left(\begin{array}{ccc}{g}_{\mathrm{xa}1}& ...& g_{\mathrm{xa}10}\\ g_{\mathrm{ya}1}& ...& g_{\mathrm{ya}10}\\ g_{\mathrm{za}1}& ...& g_{\mathrm{za}10}\end{array}\right);$ G ^TTransposition for G; $R=\left(\begin{array}{ccc}{g}_{\mathrm{xm}1}-g_{x0}& ...& g_{\mathrm{xm}10}-g_{x0}\\ g_{\mathrm{ym}1}-g_{y0}& ...& g_{\mathrm{ym}10}-g_{y0}\\ g_{\mathrm{zm}1}-g_{z0}& ...& g_{\mathrm{zm}10}-g_{z0}\end{array}\right)$

In the formula, g _Xa1... g _Xa10, g _Ya1... g _Ya10, g _Za1... g _Za10Be gravity acceleration g projection under carrier coordinate system under the 1st to the 10th position; g _Xm1... g _Xm10, g _Ym1... g _Ym10, g _Zm1... g _Zm10Be accelerometer x, y, z axle measured value under the 1st to the 10th position.

Step 4 is obtained zero drift g _X0, g _Y0, g _Z0And in the step 5 in the value substitution formula (2) of the coupled matrix S of alignment error and scale factor, just can make up formula (2) error model, thereby can be to the measured value g of accelerometer _Xm, g _Ym, g _Zm, effectively revise, obtain revised gravity acceleration g projection components g under carrier coordinate system _Xa, g _Ya, g _ZaThereby, improved the precision of measuring.

Non-linear least square that carries out in above-mentioned steps 4 and the step 5 and linear least-squares all need the correlativity between 10 positions at carrier place in step 1, the step 2 little, i.e. 10 groups of (g _Xa, g _Ya, g _Za) between, 10 groups of (g _Xm, g _Ym, g _Zm) between correlativity little.The present invention adopts as upper/lower positions choosing method (with the different position of difference representative of the angle of pitch, roll angle), and is as shown in table 1.

Table 1 10 choice of location schemes one

Attitude angle	1	2	3	4	5	6	7	8	9	10
											The angle of pitch/(°)	0	-20	40	-60	80	-100	120	-140	160	-180
Roll angle/(°)	-10	?30	-50	?70	-90	?110	-130	150	-170	10

Such scheme satisfies the correlativity requirement, and under this choosing method the stated accuracy height.Simulating, verifying to this location schemes is as follows: through mathematical software MATLAB program verification, carries out calibration experiment,, illustrates that then 10 calibration position are uncorrelated if can pick out parameter such as zero drift accurately according to location schemes, otherwise otherwise.Carry out 3000 experiments in the proof procedure altogether, record wherein can accurately pick out and waits to ask the evaluation index of the experiment number of parameter as scheme, and chooses 10 different location schemes and compare result such as table 5.

The scheme two of 10 choice of location such as table 2 is as follows:

Scheme two is chosen in table 2 10 positions

Attitude angle	1	2	3	4	5	6	7	8	9	10
											The angle of pitch/(°)	0	-20	40	-60	80	-100	120	-140	160	-180
Roll angle/(°)	0	30	-50	70	-90	110	-130	150	-170	10

The scheme three of 10 choice of location such as table 3 is as follows:

Scheme three is chosen in table 3 10 positions

Attitude angle	1	2	3	4	5	6	7	8	9	10
											The angle of pitch/(°)	0	-20	40	-60	80	-100	120	-140	160	-180
Roll angle/(°)	-10	10	-30	50	-70	90	-110	130	-150	170

The scheme four of 10 choice of location such as table 4 is as follows:

Scheme four is chosen in table 4 10 positions

Attitude angle	1	2	3	4	5	6	7	8	9	10
											The angle of pitch/(°)	0	-20	40	-60	80	-100	120	-140	160	-180
Roll angle/(°)	0	-30	50	-70	90	-110	130	-150	170	-10

10 choice of location are respectively carried out 3000 experiments under four kinds of schemes, the statistics that can accurately pick out the experiment number of waiting to ask parameter under each scheme is as shown in table 5:

Table 5 comparing result

As can be seen from Table 5,10 choice of location accurately pick out and wait to ask the experiment number of parameter the highest, so selection scheme one are a preferred version under the situation of scheme one.

Claims (4)

1. the scaling method of an accelerometer under unsupported state is characterized in that: need at first before carrying out calibration process to consider that to the most serious error parameter of accelerometer performance impact the error model of simplifying three axis accelerometer is:

$\left(\begin{array}{c}{g}_{\mathrm{xa}}\\ g_{\mathrm{ya}}\\ g_{\mathrm{za}}\end{array}\right)=\left(\begin{array}{ccc}{K}_{11}{k}_x& K_{12}{k}_y& K_{13}{k}_z\\ K_{21}{k}_x& K_{22}{k}_y& K_{23}{k}_z\\ K_{31}{k}_x& K_{32}{k}_y& K_{33}{k}_z\end{array}\right)\left(\begin{array}{c}(g_{\mathrm{xm}}-g_{x0})\\ (g_{\mathrm{ym}}-g_{y0})\\ (g_{\mathrm{zm}}-g_{z0})\end{array}\right)---\left(1\right)$

Wherein, k _x, k _y, k _zBe accelerometer x, y, z axle scale factor; K ₁₁, K ₁₂, K ₁₃, K ₂₁, K ₂₂, K ₂₃, K ₃₁, K ₃₂And K ₃₃Be the alignment error matrix element; g _X0, g _Y0, g _Z0Be accelerometer x, y, z axle zero drift; g _Xm, g _Ym, g _ZmBe accelerometer x, y, z axle measured value; g _Xa, g _Ya, g _ZaCalculated value for gravity acceleration g projection components under carrier coordinate system; $\left(\begin{array}{ccc}{K}_{11}{k}_x& K_{12}{k}_y& K_{13}{k}_z\\ K_{21}{k}_x& K_{22}{k}_y& K_{23}{k}_z\\ K_{31}{k}_x& K_{32}{k}_y& K_{33}{k}_z\end{array}\right)$ Coupled matrix for alignment error and scale factor;

And then finish demarcation by following 5 steps:

Step 1: quiet pedestal coarse alignment obtains carrier roll angle γ, pitching angle theta;

Step 2: utilize Kalman filtering to carry out quiet pedestal fine alignment, improve the alignment precision of roll angle γ, pitching angle theta, and obtain the calculated value (g of three components of the projection of gravity acceleration g under carrier coordinate system _Xa, g _Ya, g _Za);

Step 3: carrier is placed on the different position of 10 angles of pitch, roll angle carries out step 1 and step 2, judge on 10 positions, to place and whether finish, change step 1 and carry out, then obtain 10 groups of accelerometer x, y, z axle measured value (g as if finishing if finish _Xm, g _Ym, g _Zm) and the calculated value (g of three components of 10 groups of gravity acceleration g projections under carrier coordinate system _Xa, g _Ya, g _Za), continue step 4;

Step 4: three zero drift g that obtain accelerometer by nonlinear least square method _X0, g _Y0, g _Z0

Step 5: the coupled matrix that obtains alignment error and scale factor by linear least square $\left(\begin{array}{ccc}{K}_{11}{k}_x& K_{12}{k}_y& K_{13}{k}_z\\ K_{21}{k}_x& K_{22}{k}_y& K_{23}{k}_z\\ K_{31}{k}_x& K_{32}{k}_y& K_{33}{k}_z\end{array}\right);$

With the zero drift g that obtains in the step 4 _X0, g _Y0, g _Z0, and in the value substitution formula (1) of the coupled matrix of alignment error and scale factor, structure formula (1) error model is realized the demarcation of accelerometer under unsupported state.

2. a kind of scaling method of accelerometer under unsupported state according to claim 1, it is characterized in that: described three zero drifts of step 4 obtain by nonlinear least square method, specifically may further comprise the steps:

Step a, establishing target function;

With formula (1) distortion, make objective function f (p)

f(p)＝[K ₁₁k _x(g _xm-g _x0)+K ₁₂k _y(g _ym-g _y0)+K ₁₃k _z(g _zm-g _z0)] ²+[K ₂₁k _x(g _xm-g _x0)+K ₂₂k _y(g _ym-g _y0)+K ₂₃k _z(g _zm-g _z0)] ² (2)

+[K ₃₁k _x(g _xm-g _x0)+K ₃₂k _y(g _ym-g _y0)+K ₃₃k _z(g _zm-g _z0)] ²-(g _xa ²+g _ya ²+g _za ²)

Wherein, vector

p＝[g _x0，g _y0，g _z0，K ₁₁k _x，K ₁₂k _y，K ₁₃k _z，K ₂₁k _x，K ₂₂k _y，K ₂₃k _z，K ₃₁k _x，K ₃₂k _y，K ₃₃k _z]；

Step b, ask the Jacobi matrix of objective function f (p);

The Jacobi matrix J of objective function f (p) is:

Wherein, f ₁... f ₁₀Be the objective function f (p) under the 1st to the 10th position; p ₁P ₁₂Be vectorial p=[g _X0, g _Y0, g _Z0, S ₁₁, S ₁₂, S ₁₃, S ₂₁, S ₂₂, S ₂₃, S ₃₁, S ₃₂, S ₃₃] in the 1st to the 12nd element;

Step c, iterative approach unknown vector p;

Solve an equation:

$(J_k^T{J}_k+v_{k}I){\mathrm{\δ}}^{\left(k\right)}=-J_k^T{f}^{\left(k\right)}---\left(4\right)$

Obtain vectorial p k step correction δ ^(k)

Wherein, J _kBe Jacobi matrix J k step updating value, k=1,2,

Be J _kTransposition; v _kBe adjustable iteration step length; I is 12 rank unit matrix;

Be objective function f (p) the renewal result in k step when the 1st to the 10th position;

By

p ^(k+1)＝p ^(k)+δ ^(k) (5)

Wherein, p ^(k+1)Be vectorial p k+1 step updating value; p ^(k)Be vectorial p k step updating value; To formula (2), (3), (4), (5) find the solution iteration repeatedly, converge to stationary value up to vectorial p; First three element g of vector p _X0, g _Y0, g _Z0It is exactly the zero drift of accelerometer.

3. a kind of scaling method of accelerometer under unsupported state according to claim 1, it is characterized in that: the coupled matrix of described alignment error of step 5 and scale factor obtains by linear least square, specifically comprises with following step:

With zero drift g _X0, g _Y0, g _Z0Bring formula (1) into, formula (1) error model is degenerated into linearity, utilize linear least square to try to achieve coupled matrix $\left(\begin{array}{ccc}{K}_{11}{k}_x& K_{12}{k}_y& K_{13}{k}_z\\ K_{21}{k}_x& K_{22}{k}_y& K_{23}{k}_z\\ K_{31}{k}_x& K_{32}{k}_y& K_{33}{k}_z\end{array}\right)$ For:

$\left(\begin{array}{ccc}{K}_{11}{k}_x& K_{12}{k}_y& K_{13}{k}_z\\ K_{21}{k}_x& K_{22}{k}_y& K_{23}{k}_z\\ K_{31}{k}_x& K_{32}{k}_y& K_{33}{k}_z\end{array}\right)={(R*(G^T*{(G*G^T)}^{-1}))}^{-1}---\left(6\right)$

Wherein:

$G=\left(\begin{array}{ccc}{g}_{\mathrm{xa}1}& ...& g_{\mathrm{xa}10}\\ g_{\mathrm{ya}1}& ...& g_{\mathrm{ya}10}\\ g_{\mathrm{za}1}& ...& g_{\mathrm{za}10}\end{array}\right);$ G ^TTransposition for G; $R=\left(\begin{array}{ccc}{g}_{\mathrm{xm}1}-g_{x0}& ...& g_{\mathrm{xm}10}-g_{x0}\\ g_{\mathrm{ym}1}-g_{y0}& ...& g_{\mathrm{ym}10}-g_{y0}\\ g_{\mathrm{zm}1}-g_{z0}& ...& g_{\mathrm{zm}10}-g_{z0}\end{array}\right)$

In the formula, g _Xa1G _Xa10, g _Ya1G _Ya10, g _Za1G _Za10Be gravity acceleration g projection under carrier coordinate system under the 1st to the 10th position; g _Xm1G _Xm10, g _Ym1G _Ym10, g _Zm1G _Zm10Be carrier accelerometer x, y, z axle measured value under the 1st to the 10th position.

4. a kind of scaling method of accelerometer under unsupported state according to claim 1, it is characterized in that: choose the angle of pitch and roll angle be respectively (0 ° ,-10 °), (20 °, 30 °), (40 °,-50 °) (60 °, 70 °), (80 ° ,-90 °), (100 °, 110 °), (120 °,-130 °), (140 °, 150 °), (160 ° ,-170 °), (180 °, 10 °) are 10 positions at carrier place.

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