CN105241474A - Inclined-configuration inertial navigation system calibration method - Google Patents

Abstract

The invention belongs to the technical field of navigation and relates to a calibration method of an inertial navigation system with an inclined sensitive shaft. In the technical scheme, a normalized orthogonal method is employed to convert an inclined gyroscope and an inclined accelerometer sensitive shaft onto a projectile axis through a direction cosine matrix, so that a virtual gyroscope coordinate system and an accelerometer coordinate system and the real projectile coordinate system coincide together, thereby solving a problem of parameter identification of the inertial navigation system with the inclined sensitive shaft.

Description

A kind of tilting configuration inertial navigation system scaling method

Technical field

The invention belongs to field of navigation technology, relate to the scaling method of the tilting inertial navigation system of a kind of sensitive axes.

Background technology

Strapdown inertial navitation system (SINS) adopts redundancy technology to improve reliability and the precision of system, inertial sensor part many employings tilted configuration usually.And for nonredundant inertial navigation system, its Sensitive Apparatus also can adopt tilting, its advantage is to expand carrier three axial angular velocity and acceleration analysis scope, saves the installing space of inertia device.But this mounting means brings difficulty to the demarcation of inertial measurement unit.Conventional scaling method requires that inertia device is installed along orthogonal carrier coordinate system, by the position test on turntable, speed trial, and the parameters of identification inertia device.

Therefore, need a kind of tilting configuration inertial navigation system scaling method of development badly, both can at strapdown inertial navitation system (SINS) or nonredundant inertial navigation system medium dip configuration inertial sensor part, again can accurately, the parameters of the tilting inertial navigation system of Fast Identification sensitive axes, convenient inertial navigation system to be demarcated.

Summary of the invention

The object of the present invention is to provide a kind of tilting configuration inertial navigation system scaling method, thus accurately, the parameters of the tilting inertial navigation system of Fast Identification sensitive axes.

In order to realize this purpose, the technical scheme that the present invention takes is as follows:

A kind of tilting configuration inertial navigation system scaling method, specifically comprises the following steps:

One, inertial navigation system gyroscope, accelerometer are configured

Inertial navigation system three non-orthogonal gyroscopes are set and are respectively G ₁, G ₂, G ₃, three orthogonal body axles are respectively OX _b, OY _b, OZ _b; Gyrostatic three input shaft OG ₁, OG ₂, OG ₃be evenly distributed on+OY _bcentered by, with+OY _bthe angle of axle is on the circular conical surface of α, and adjacent gyrostatic two input shafts are at OX _bz _bprojection angle in plane is 120 °, wherein, and OG ₁at OX _bz _bprojection in plane and+OX _boverlap;

Three non-orthogonal accelerometers are respectively A ₁, A ₂, A ₃, three input shaft OA of accelerometer ₁, OA ₂, OA ₃be evenly distributed on+OY _bcentered by, with+OY _baxle clamp angle is on the circular conical surface of β, and two input shafts of adjacent accelerometer are at OX _bz _bprojection angle in plane is 120 °, wherein, and OA ₁at OX _bz _bprojection in plane and+OX _boverlap;

Wherein, alpha+beta=90 °; In this specific embodiment: α is 54.73 °, β is 35.27 °.

Two, respectively normalization is exported to gyroscope, accelerometer

Setting gyroscope G ₁, G ₂, G ₃, accelerometer A ₁, A ₂, A ₃the dimension exported is LSB/s;

Before demarcation, gyrostatic output dimension to be converted into °/s, the output dimension of accelerometer transforms g;

The output normalization formula of gyroscope, accelerometer is as follows:

$N_{\mathrm{gx}1}=({\stackrel{\‾}{N}}_{g1}-{\stackrel{\‾}{D}}_{f1})/{\stackrel{\‾}{S}}_{g1}$

$N_{g2}=({\stackrel{\‾}{N}}_{g2}-{\stackrel{\‾}{D}}_{f2})/{\stackrel{\‾}{S}}_{g2}$

$N_{g3}=({\stackrel{\‾}{N}}_{g3}-{\stackrel{\‾}{D}}_{f3})/{\stackrel{\‾}{S}}_{g3}$

$N_{a1}=({\stackrel{\‾}{N}}_{a1}-{\stackrel{\‾}{K}}_{a10})/{\stackrel{\‾}{S}}_{a1}$

$N_{a2}=({\stackrel{\‾}{N}}_{a2}-{\stackrel{\‾}{K}}_{a20})/{\stackrel{\‾}{S}}_{a2}$

$N_{a3}=({\stackrel{\‾}{N}}_{a3}-{\stackrel{\‾}{K}}_{a30})/{\stackrel{\‾}{S}}_{a3}$

In formula:

---gyroscope G ₁, G ₂, G ₃original output umber of pulse, unit: LSB/s;

---gyroscope G ₁, G ₂, G ₃zero-bit, unit: LSB/s;

---gyroscope G ₁, G ₂, G ₃constant multiplier, unit: (LSB/s)/(°/s);

N _gx1, N _g2, N _g3---gyroscope G ₁, G ₂, G ₃export after normalization, unit: °/s;

---accelerometer A ₁, A ₂, A ₃original output umber of pulse, unit: LSB/s;

---accelerometer A ₁, A ₂, A ₃zero-bit, unit: LSB/s;

---accelerometer A ₁, A ₂, A ₃constant multiplier, unit: (LSB/s)/g;

N _a1, N _a2, N _a3---accelerometer A ₁, A ₂, A ₃export after normalization, unit: g;

After normalized, gyroscope G ₁, G ₂, G ₃accelerometer A ₁, A ₂, A ₃output remains non-orthogonal;

Three, gyroscope, accelerometer output orthogonal

(3.1) to gyroscope output orthogonal

Determine O-X _by _bz _bwith O-G ₁g ₂g ₃between transition matrix:

$\left[\begin{array}{c}{N}_{\mathrm{gx}}\\ N_{\mathrm{gy}}\\ N_{\mathrm{gz}}\end{array}\right]{=T}_g\·\left[\begin{array}{c}{N}_{g1}\\ N_{g2}\\ N_{g3}\end{array}\right]$

In formula:

O-N _g1n _g2n _g3---the gyroscope G obtained in step 2 ₁, G ₂, G ₃export after normalization;

O-N _gxn _gyn _gz---with body system O-X _by _bz _boverlap, virtual gyro coordinate system;

Through as above formula, non-orthogonal gyro coordinate system O-G ₁g ₂g ₃by transition matrix T _gbe transformed into the virtual gyro coordinate system O-N be orthogonal _gxn _gyn _gz;

(3.2) to accelerometer output orthogonal

Determine O-X _by _bz _bwith O-A ₁a ₂a ₃between transition matrix:

$\left[\begin{array}{c}{N}_{\mathrm{ax}}\\ N_{\mathrm{ay}}\\ N_{\mathrm{az}}\end{array}\right]{=T}_a\·\left[\begin{array}{c}{N}_{a1}\\ N_{a2}\\ N_{a3}\end{array}\right]$

In formula:

O-N _a1n _a2n _a3---the accelerometer A obtained in step 2 ₁, A ₂, A ₃export after normalization;

O-N _axn _ayn _az---with body system O-X _by _bz _bthat overlap, virtual accelerometer coordinate system;

Through as above formula, non-orthogonal accelerometer coordinate system O-A ₁a ₂a ₃the virtual accelerometer coordinate system O-N be orthogonal is transformed into by transition matrix Ta _axn _ayn _az;

Four, inertial navigation system mathematical model is determined

After orthonormalization, inertial navigation system mathematical model is as follows:

$\left[\begin{array}{c}{N}_{\mathrm{gx}}\\ N_{\mathrm{gy}}\\ N_{\mathrm{gz}}\end{array}\right]=\left[\begin{array}{c}{D}_{\mathrm{fx}}\\ D_{\mathrm{fy}}\\ D_{\mathrm{fz}}\end{array}\right]+\left[\begin{array}{ccc}{S}_{\mathrm{gx}}& 0& 0\\ 0& S_{\mathrm{gy}}& 0\\ 0& 0& S_{\mathrm{gz}}\end{array}\right]\×\left[\begin{array}{c}{\mathrm{\ω}}_x\\ {\mathrm{\ω}}_y\\ {\mathrm{\ω}}_z\end{array}\right]+\left[\begin{array}{ccc}0& K_{\mathrm{gyx}}& K_{\mathrm{gzx}}\\ K_{\mathrm{gxy}}& 0& K_{\mathrm{gzy}}\\ K_{\mathrm{gxz}}& K_{\mathrm{gyz}}& 0\end{array}\right]\×\left[\begin{array}{c}{\mathrm{\ω}}_x\\ {\mathrm{\ω}}_y\\ {\mathrm{\ω}}_z\end{array}\right]+\left[\begin{array}{ccc}{D}_{\mathrm{ix}}& D_{\mathrm{ox}}& D_{\mathrm{sx}}\\ D_{\mathrm{oy}}& D_{\mathrm{iy}}& D_{\mathrm{sy}}\\ D_{\mathrm{oz}}& D_{\mathrm{sz}}& D_{\mathrm{iz}}\end{array}\right]\×\left[\begin{array}{c}{A}_x\\ A_y\\ A_z\end{array}\right]$

In formula:

N _gx, N _gy, N _gz---the output of gyro passage in virtual gyro coordinate system in each coordinate axis;

D _fx, D _fy, D _fz---the constant value drift of gyro passage in virtual gyro coordinate system in each coordinate axis;

S _gx, S _gy, S _gz---the constant multiplier of gyro passage in virtual gyro coordinate system in each coordinate axis;

K _gij---i direction of principal axis is to the gyrostatic alignment error coefficient of j;

D _ix---the impact that the motion of X axis line exports gyro in X-axis;

D _iy---the impact that the motion of X axis line exports gyro in Y-axis;

D _iz---the impact that the motion of X axis line exports gyro on Z axis;

D _ox---the impact that the motion of Y-axis line exports gyro in X-axis;

D _oy---the impact that the motion of Y-axis line exports gyro in Y-axis;

D _oz---the impact that the motion of Y-axis line exports gyro on Z axis;

D _sx---the impact that the motion of Z-axis direction line exports gyro in X-axis;

D _sy---the impact that the motion of Z-axis direction line exports gyro in Y-axis;

D _sz---the impact that the motion of Z-axis direction line exports gyro on Z axis;

$\left[\begin{array}{c}{N}_{\mathrm{ax}}\\ N_{\mathrm{ay}}\\ N_{\mathrm{az}}\end{array}\right]=\left[\begin{array}{c}{K}_{a0x}\\ K_{a0y}\\ K_{a0z}\end{array}\right]+\left[\begin{array}{ccc}{K}_{a1x}& 0& 0\\ 0& K_{a1y}& 0\\ 0& 0& K_{a1z}\end{array}\right]\×\left[\begin{array}{c}{A}_x\\ A_y\\ A_z\end{array}\right]+\left[\begin{array}{ccc}0& K_{\mathrm{ayx}}& K_{\mathrm{azx}}\\ K_{\mathrm{axy}}& 0& K_{\mathrm{azy}}\\ K_{\mathrm{axz}}& K_{\mathrm{ayz}}& 0\end{array}\right]\×\left[\begin{array}{c}{A}_x\\ A_y\\ A_z\end{array}\right]+\left[\begin{array}{ccc}{K}_{a2x}& 0& 0\\ 0& K_{a2y}& 0\\ 0& 0& K_{a2z}\end{array}\right]\×\left[\begin{array}{c}{A}_x^2\\ A_y^2\\ A_z^2\end{array}\right]$

In formula:

N _ax, N _ay, N _az---the pulse of accelerometer passage in each coordinate axis of virtual accelerometer coordinate system exports;

K _ax0, K _ay0, K _az0---the inclined value of accelerometer passage in each coordinate axis of virtual accelerometer coordinate system;

K _aij---i axle is to the alignment error coefficient of j accelerometer passage;

K _a1x, K _a1y, K _a1z---the constant multiplier of accelerometer passage in each coordinate axis of virtual accelerometer coordinate system.

Further, a kind of tilting configuration inertial navigation system scaling method as above, wherein: α is 54.73 °, β is 35.27 °.

The beneficial effect of technical solution of the present invention is, by adopting the method for orthonormalization, tilting gyro, accelerometer sensitive axle are transformed on body axle by direction cosine matrix, virtual gyro coordinate system, accelerometer coordinate system are overlapped with real body system, thus method solve the parameter identification problem of the tilting inertial navigation system of sensitive axes.

Embodiment

Below in conjunction with specific embodiment, technical solution of the present invention is described in detail.

A kind of tilting configuration inertial navigation system scaling method, specifically comprises the following steps:

One, inertial navigation system gyroscope, accelerometer are configured

Inertial navigation system three non-orthogonal gyroscopes are set and are respectively G ₁, G ₂, G ₃, three orthogonal body axles are respectively OX _b, OY _b, OZ _b; Gyrostatic three input shaft OG ₁, OG ₂, OG ₃be evenly distributed on+OY _bcentered by, with+OY _bthe angle of axle is on the circular conical surface of α, and adjacent gyrostatic two input shafts are at OX _bz _bprojection angle in plane is 120 °, wherein, and OG ₁at OX _bz _bprojection in plane and+OX _boverlap;

Three non-orthogonal accelerometers are respectively A ₁, A ₂, A ₃, three input shaft OA of accelerometer ₁, OA ₂, OA ₃be evenly distributed on+OY _bcentered by, with+OY _baxle clamp angle is on the circular conical surface of β, and two input shafts of adjacent accelerometer are at OX _bz _bprojection angle in plane is 120 °, wherein, and OA ₁at OX _bz _bprojection in plane and+OX _boverlap;

Wherein, alpha+beta=90 °;

Two, respectively normalization is exported to gyroscope, accelerometer

Setting gyroscope G ₁, G ₂, G ₃, accelerometer A ₁, A ₂, A ₃the dimension exported is LSB/s;

Before demarcation, gyrostatic output dimension to be converted into °/s, the output dimension of accelerometer transforms g;

The output normalization formula of gyroscope, accelerometer is as follows:

$N_{\mathrm{gx}1}=({\stackrel{\‾}{N}}_{g1}-{\stackrel{\‾}{D}}_{f1})/{\stackrel{\‾}{S}}_{g1}$

$N_{g2}=({\stackrel{\‾}{N}}_{g2}-{\stackrel{\‾}{D}}_{f2})/{\stackrel{\‾}{S}}_{g2}$

$N_{g3}=({\stackrel{\‾}{N}}_{g3}-{\stackrel{\‾}{D}}_{f3})/{\stackrel{\‾}{S}}_{g3}$

$N_{a1}=({\stackrel{\‾}{N}}_{a1}-{\stackrel{\‾}{K}}_{a10})/{\stackrel{\‾}{S}}_{a1}$

$N_{a2}=({\stackrel{\‾}{N}}_{a2}-{\stackrel{\‾}{K}}_{a20})/{\stackrel{\‾}{S}}_{a2}$

$N_{a3}=({\stackrel{\‾}{N}}_{a3}-{\stackrel{\‾}{K}}_{a30})/{\stackrel{\‾}{S}}_{a3}$

In formula:

---gyroscope G ₁, G ₂, G ₃original output umber of pulse, unit: LSB/s;

---gyroscope G ₁, G ₂, G ₃zero-bit, unit: LSB/s;

---gyroscope G ₁, G ₂, G ₃constant multiplier, unit: (LSB/s)/(°/s);

N _gx1, N _g2, N _g3---gyroscope G ₁, G ₂, G ₃export after normalization, unit: °/s;

---accelerometer A ₁, A ₂, A ₃original output umber of pulse, unit: LSB/s;

---accelerometer A ₁, A ₂, A ₃zero-bit, unit: LSB/s;

---accelerometer A ₁, A ₂, A ₃constant multiplier, unit: (LSB/s)/g;

N _a1, N _a2, N _a3---accelerometer A ₁, A ₂, A ₃export after normalization, unit: g;

After normalized, gyroscope G ₁, G ₂, G ₃accelerometer A ₁, A ₂, A ₃output remains non-orthogonal;

Three, gyroscope, accelerometer output orthogonal

(3.1) to gyroscope output orthogonal

Determine O-X _by _bz _bwith O-G ₁g ₂g ₃between transition matrix:

$\left[\begin{array}{c}{N}_{\mathrm{gx}}\\ N_{\mathrm{gy}}\\ N_{\mathrm{gz}}\end{array}\right]{=T}_g\·\left[\begin{array}{c}{N}_{g1}\\ N_{g2}\\ N_{g3}\end{array}\right]$

In formula:

O-N _g1n _g2n _g3---the gyroscope G obtained in step 2 ₁, G ₂, G ₃export after normalization;

O-N _gxn _gyn _gz---with body system O-X _by _bz _boverlap, virtual gyro coordinate system;

Through as above formula, non-orthogonal gyro coordinate system O-G ₁g ₂g ₃by transition matrix T _gbe transformed into the virtual gyro coordinate system O-N be orthogonal _gxn _gyn _gz;

(3.2) to accelerometer output orthogonal

Determine O-X _by _bz _bwith O-A ₁a ₂a ₃between transition matrix:

$\left[\begin{array}{c}{N}_{\mathrm{ax}}\\ N_{\mathrm{ay}}\\ N_{\mathrm{az}}\end{array}\right]{=T}_a\·\left[\begin{array}{c}{N}_{a1}\\ N_{a2}\\ N_{a3}\end{array}\right]$

In formula:

O-N _a1n _a2n _a3---the accelerometer A obtained in step 2 ₁, A ₂, A ₃export after normalization;

O-N _axn _ayn _az---with body system O-X _by _bz _bthat overlap, virtual accelerometer coordinate system;

Through as above formula, non-orthogonal accelerometer coordinate system O-A ₁a ₂a ₃the virtual accelerometer coordinate system O-N be orthogonal is transformed into by transition matrix Ta _axn _ayn _az;

Four, inertial navigation system mathematical model is determined

After orthonormalization, inertial navigation system mathematical model is as follows:

$\left[\begin{array}{c}{N}_{\mathrm{gx}}\\ N_{\mathrm{gy}}\\ N_{\mathrm{gz}}\end{array}\right]=\left[\begin{array}{c}{D}_{\mathrm{fx}}\\ D_{\mathrm{fy}}\\ D_{\mathrm{fz}}\end{array}\right]+\left[\begin{array}{ccc}{S}_{\mathrm{gx}}& 0& 0\\ 0& S_{\mathrm{gy}}& 0\\ 0& 0& S_{\mathrm{gz}}\end{array}\right]\×\left[\begin{array}{c}{\mathrm{\ω}}_x\\ {\mathrm{\ω}}_y\\ {\mathrm{\ω}}_z\end{array}\right]+\left[\begin{array}{ccc}0& K_{\mathrm{gyx}}& K_{\mathrm{gzx}}\\ K_{\mathrm{gxy}}& 0& K_{\mathrm{gzy}}\\ K_{\mathrm{gxz}}& K_{\mathrm{gyz}}& 0\end{array}\right]\×\left[\begin{array}{c}{\mathrm{\ω}}_x\\ {\mathrm{\ω}}_y\\ {\mathrm{\ω}}_z\end{array}\right]+\left[\begin{array}{ccc}{D}_{\mathrm{ix}}& D_{\mathrm{ox}}& D_{\mathrm{sx}}\\ D_{\mathrm{oy}}& D_{\mathrm{iy}}& D_{\mathrm{sy}}\\ D_{\mathrm{oz}}& D_{\mathrm{sz}}& D_{\mathrm{iz}}\end{array}\right]\×\left[\begin{array}{c}{A}_x\\ A_y\\ A_z\end{array}\right]$

In formula:

N _gx, N _gy, N _gz---the output of gyro passage in virtual gyro coordinate system in each coordinate axis;

D _fx, D _fy, D _fz---the constant value drift of gyro passage in virtual gyro coordinate system in each coordinate axis;

S _gx, S _gy, S _gz---the constant multiplier of gyro passage in virtual gyro coordinate system in each coordinate axis;

K _gij---i direction of principal axis is to the gyrostatic alignment error coefficient of j;

D _ix---the impact that the motion of X axis line exports gyro in X-axis;

D _iy---the impact that the motion of X axis line exports gyro in Y-axis;

D _iz---the impact that the motion of X axis line exports gyro on Z axis;

D _ox---the impact that the motion of Y-axis line exports gyro in X-axis;

D _oy---the impact that the motion of Y-axis line exports gyro in Y-axis;

D _oz---the impact that the motion of Y-axis line exports gyro on Z axis;

D _sx---the impact that the motion of Z-axis direction line exports gyro in X-axis;

D _sy---the impact that the motion of Z-axis direction line exports gyro in Y-axis;

D _sz---the impact that the motion of Z-axis direction line exports gyro on Z axis;

$\left[\begin{array}{c}{N}_{\mathrm{ax}}\\ N_{\mathrm{ay}}\\ N_{\mathrm{az}}\end{array}\right]=\left[\begin{array}{c}{K}_{a0x}\\ K_{a0y}\\ K_{a0z}\end{array}\right]+\left[\begin{array}{ccc}{K}_{a1x}& 0& 0\\ 0& K_{a1y}& 0\\ 0& 0& K_{a1z}\end{array}\right]\×\left[\begin{array}{c}{A}_x\\ A_y\\ A_z\end{array}\right]+\left[\begin{array}{ccc}0& K_{\mathrm{ayx}}& K_{\mathrm{azx}}\\ K_{\mathrm{axy}}& 0& K_{\mathrm{azy}}\\ K_{\mathrm{axz}}& K_{\mathrm{ayz}}& 0\end{array}\right]\×\left[\begin{array}{c}{A}_x\\ A_y\\ A_z\end{array}\right]+\left[\begin{array}{ccc}{K}_{a2x}& 0& 0\\ 0& K_{a2y}& 0\\ 0& 0& K_{a2z}\end{array}\right]\×\left[\begin{array}{c}{A}_x^2\\ A_y^2\\ A_z^2\end{array}\right]$

In formula:

N _ax, N _ay, N _az---the pulse of accelerometer passage in each coordinate axis of virtual accelerometer coordinate system exports;

K _ax0, K _ay0, K _az0---the inclined value of accelerometer passage in each coordinate axis of virtual accelerometer coordinate system;

K _aij---i axle is to the alignment error coefficient of j accelerometer passage;

K _a1x, K _a1y, K _a1z---the constant multiplier of accelerometer passage in each coordinate axis of virtual accelerometer coordinate system.

Claims (2)

1. a tilting configuration inertial navigation system scaling method, is characterized in that, specifically comprise the following steps:

(1) inertial navigation system gyroscope, accelerometer are configured

Inertial navigation system three non-orthogonal gyroscopes are set and are respectively G ₁, G ₂, G ₃, three orthogonal body axles are respectively OX _b, OY _b, OZ _b; Gyrostatic three input shaft OG ₁, OG ₂, OG ₃be evenly distributed on+OY _bcentered by, with+OY _bthe angle of axle is on the circular conical surface of α, and adjacent gyrostatic two input shafts are at OX _bz _bprojection angle in plane is 120 °, wherein, and OG ₁at OX _bz _bprojection in plane and+OX _boverlap;

Three non-orthogonal accelerometers are respectively A ₁, A ₂, A ₃, three input shaft OA of accelerometer ₁, OA ₂, OA ₃be evenly distributed on+OY _bcentered by, with+OY _baxle clamp angle is on the circular conical surface of β, and two input shafts of adjacent accelerometer are at OX _bz _bprojection angle in plane is 120 °, wherein, and OA ₁at OX _bz _bprojection in plane and+OX _boverlap;

Wherein, alpha+beta=90 °;

(2) respectively normalization is exported to gyroscope, accelerometer

Setting gyroscope G ₁, G ₂, G ₃, accelerometer A ₁, A ₂, A ₃the dimension exported is LSB/s;

Before demarcation, gyrostatic output dimension to be converted into °/s, the output dimension of accelerometer transforms g;

The output normalization formula of gyroscope, accelerometer is as follows:

$N_{\mathrm{gx}1}=({\stackrel{\‾}{N}}_{g1}-{\stackrel{\‾}{D}}_{f1})/{\stackrel{\‾}{S}}_{g1}$

$N_{g2}=({\stackrel{\‾}{N}}_{g2}-{\stackrel{\‾}{D}}_{f2})/{\stackrel{\‾}{S}}_{g2}$

$N_{g3}=({\stackrel{\‾}{N}}_{g3}-{\stackrel{\‾}{D}}_{f3})/{\stackrel{\‾}{S}}_{g3}$

$N_{a1}=({\stackrel{\‾}{N}}_{a1}-{\stackrel{\‾}{K}}_{a10})/{\stackrel{\‾}{S}}_{a1}$

$N_{a2}=({\stackrel{\‾}{N}}_{a2}-{\stackrel{\‾}{K}}_{a20})/{\stackrel{\‾}{S}}_{a2}$

$N_{a3}=({\stackrel{\‾}{N}}_{a3}-{\stackrel{\‾}{K}}_{a30})/{\stackrel{\‾}{S}}_{a3}$

In formula:

---gyroscope G ₁, G ₂, G ₃original output umber of pulse, unit: LSB/s;

---gyroscope G ₁, G ₂, G ₃zero-bit, unit: LSB/s;

---gyroscope G ₁, G ₂, G ₃constant multiplier, unit: (LSB/s)/(°/s);

N _gx1, N _g2, N _g3---gyroscope G ₁, G ₂, G ₃export after normalization, unit: °/s;

---accelerometer A ₁, A ₂, A ₃original output umber of pulse, unit: LSB/s;

---accelerometer A ₁, A ₂, A ₃zero-bit, unit: LSB/s;

---accelerometer A ₁, A ₂, A ₃constant multiplier, unit: (LSB/s)/g;

N _a1, N _a2, N _a3---accelerometer A ₁, A ₂, A ₃export after normalization, unit: g;

After normalized, gyroscope G ₁, G ₂, G ₃accelerometer A ₁, A ₂, A ₃output remains non-orthogonal;

(3) gyroscope, accelerometer output orthogonal

(3.1) to gyroscope output orthogonal

Determine O-X _by _bz _bwith O-G ₁g ₂g ₃between transition matrix:

$\left[\begin{array}{c}{N}_{\mathrm{gx}}\\ N_{\mathrm{gy}}\\ N_{\mathrm{gz}}\end{array}\right]{=T}_g\·\left[\begin{array}{c}{N}_{g1}\\ N_{g2}\\ N_{g3}\end{array}\right]$

In formula:

O-N _g1n _g2n _g3---the gyroscope G obtained in step 2 ₁, G ₂, G ₃export after normalization;

O-N _gxn _gyn _gz---with body system O-X _by _bz _boverlap, virtual gyro coordinate system;

Through as above formula, non-orthogonal gyro coordinate system O-G ₁g ₂g ₃by transition matrix T _gbe transformed into the virtual gyro coordinate system O-N be orthogonal _gxn _gyn _gz;

(3.2) to accelerometer output orthogonal

Determine O-X _by _bz _bwith O-A ₁a ₂a ₃between transition matrix:

$\left[\begin{array}{c}{N}_{\mathrm{ax}}\\ N_{\mathrm{ay}}\\ N_{\mathrm{az}}\end{array}\right]{=T}_a\·\left[\begin{array}{c}{N}_{a1}\\ N_{a2}\\ N_{a3}\end{array}\right]$

In formula:

O-N _a1n _a2n _a3---the accelerometer A obtained in step 2 ₁, A ₂, A ₃export after normalization;

O-N _axn _ayn _az---with body system O-X _by _bz _bthat overlap, virtual accelerometer coordinate system;

Through as above formula, non-orthogonal accelerometer coordinate system O-A ₁a ₂a ₃the virtual accelerometer coordinate system O-N be orthogonal is transformed into by transition matrix Ta _axn _ayn _az;

(4) inertial navigation system mathematical model is determined

After orthonormalization, inertial navigation system mathematical model is as follows:

$\left[\begin{array}{c}{N}_{\mathrm{gx}}\\ N_{\mathrm{gy}}\\ N_{\mathrm{gz}}\end{array}\right]=\left[\begin{array}{c}{D}_{\mathrm{fx}}\\ D_{\mathrm{fy}}\\ D_{\mathrm{fz}}\end{array}\right]+\left[\begin{array}{ccc}{S}_{\mathrm{gx}}& 0& 0\\ 0& S_{\mathrm{gy}}& 0\\ 0& 0& S_{\mathrm{gz}}\end{array}\right]\×\left[\begin{array}{c}{\mathrm{\ω}}_x\\ {\mathrm{\ω}}_y\\ {\mathrm{\ω}}_z\end{array}\right]+\left[\begin{array}{ccc}0& K_{\mathrm{gyx}}& K_{\mathrm{gzx}}\\ K_{\mathrm{gxy}}& 0& K_{\mathrm{gzy}}\\ K_{\mathrm{gxz}}& K_{\mathrm{gyz}}& 0\end{array}\right]\×\left[\begin{array}{c}{\mathrm{\ω}}_x\\ {\mathrm{\ω}}_y\\ {\mathrm{\ω}}_z\end{array}\right]+\left[\begin{array}{ccc}{D}_{\mathrm{ix}}& D_{\mathrm{ox}}& D_{\mathrm{sx}}\\ D_{\mathrm{oy}}& D_{\mathrm{iy}}& D_{\mathrm{sy}}\\ D_{\mathrm{oz}}& D_{\mathrm{sz}}& D_{\mathrm{iz}}\end{array}\right]\×\left[\begin{array}{c}{A}_x\\ A_y\\ A_z\end{array}\right]$

In formula:

N _gx, N _gy, N _gz---the output of gyro passage in virtual gyro coordinate system in each coordinate axis;

D _fx, D _fy, D _fz---the constant value drift of gyro passage in virtual gyro coordinate system in each coordinate axis;

S _gx, S _gy, S _gz---the constant multiplier of gyro passage in virtual gyro coordinate system in each coordinate axis;

K _gij---i direction of principal axis is to the gyrostatic alignment error coefficient of j;

D _ix---the impact that the motion of X axis line exports gyro in X-axis;

D _iy---the impact that the motion of X axis line exports gyro in Y-axis;

D _iz---the impact that the motion of X axis line exports gyro on Z axis;

D _ox---the impact that the motion of Y-axis line exports gyro in X-axis;

D _oy---the impact that the motion of Y-axis line exports gyro in Y-axis;

D _oz---the impact that the motion of Y-axis line exports gyro on Z axis;

D _sx---the impact that the motion of Z-axis direction line exports gyro in X-axis;

D _sy---the impact that the motion of Z-axis direction line exports gyro in Y-axis;

D _sz---the impact that the motion of Z-axis direction line exports gyro on Z axis;

$\left[\begin{array}{c}{N}_{\mathrm{ax}}\\ N_{\mathrm{ay}}\\ N_{\mathrm{az}}\end{array}\right]=\left[\begin{array}{c}{K}_{a0x}\\ K_{a0y}\\ K_{a0z}\end{array}\right]+\left[\begin{array}{ccc}{K}_{a1x}& 0& 0\\ 0& K_{a1y}& 0\\ 0& 0& K_{a1z}\end{array}\right]\×\left[\begin{array}{c}{A}_x\\ A_y\\ A_z\end{array}\right]+\left[\begin{array}{ccc}0& K_{\mathrm{ayx}}& K_{\mathrm{azx}}\\ K_{\mathrm{axy}}& 0& K_{\mathrm{azy}}\\ K_{\mathrm{axz}}& K_{\mathrm{ayz}}& 0\end{array}\right]\×\left[\begin{array}{c}{A}_x\\ A_y\\ A_z\end{array}\right]+\left[\begin{array}{ccc}{K}_{a2x}& 0& 0\\ 0& K_{a2y}& 0\\ 0& 0& K_{a2z}\end{array}\right]\×\left[\begin{array}{c}{A}_x^2\\ A_y^2\\ A_z^2\end{array}\right]$

In formula:

N _ax, N _ay, N _az---the pulse of accelerometer passage in each coordinate axis of virtual accelerometer coordinate system exports;

K _ax0, K _ay0, K _az0---the inclined value of accelerometer passage in each coordinate axis of virtual accelerometer coordinate system;

K _aij---i axle is to the alignment error coefficient of j accelerometer passage;

K _a1x, K _a1y, K _a1z---the constant multiplier of accelerometer passage in each coordinate axis of virtual accelerometer coordinate system.

2. a kind of tilting configuration inertial navigation system scaling method as claimed in claim 1, it is characterized in that, in step (1): α is 54.73 °, β is 35.27 °.