CN102589573A - Sensor field calibration method in miniature integrated navigation system - Google Patents

Abstract

A sensor field calibration method in a miniature integrated navigation system belongs to the inertia/terrestrial magnetism integrated navigation system calibration technique. Firstly measurement models of an accelerometer, a terrestrial magnetism sensor and a gyroscope of an inertial measurement unit in the integrated navigation system are given out, main error components of the sensor in a field environment are analyzed, then a six position calibration layout method is adopted, and scale factors and zero offset correction factors of the accelerometer, the terrestrial magnetism sensor and the gyroscope are obtained through a solving equation set. The sensor field calibration method is particularly suitable to use in the field environment without standard equipment of rotary tables and the like, and is simple in operation, high in calibration accuracy and wide in applicable scope.

Description

The open-air scaling method of sensor in the minitype combined navigation system

Technical field

The invention belongs to the scaling method of inertia/earth magnetism integrated navigation system, mainly relate to the open-air scaling method of the minitype combined navigation system that a kind of accelerometer by the MEMS type, gyroscope, geomagnetic sensor constitute.

Background technology

Inertial Measurement Unit in the integrated navigation system (IMU) is that 3 accelerometers and 3 gyroscopes by the sensitive axes pairwise orthogonal constitute; Can measure the carrier movement of 6 degree of freedom; Promptly measure carrier along three orthogonal axes to acceleration and angular velocity; In order to revise its course, attitude error, cooperate three betwixt mountains Magnetic Sensors with the sensitive axes pairwise orthogonal.

Under the ideal situation, each sensitive axes pairwise orthogonal of Inertial Measurement Unit constitutes rectangular coordinate system in space, and any one output (y) is answered proportional y=kx with this axle input (x), and k is a constant multiplier; But there are the error of zero in actual use brief acceleration meter, geomagnetic sensor and gyrostatic output, and promptly zero partially; When sensor installation, 3 sensitive axes all can not be accomplished complete pairwise orthogonal in addition, therefore have alignment error; These factor affecting make each sensitive axes output of sensor not proportional with this input, i.e. y ≠ kx to the measuring accuracy of sensor.

Therefore to set up comprise zero partially, alignment error and the isoparametric sensor measurement model of constant multiplier; Find the solution parameters through calibration algorithm; With the mathematical relation that obtains being consistent with actual input and output situation; Implement compensation again, improve the measuring accuracy of sensor, thereby guarantee accuracy of navigation systems.

Because the constant multiplier of sensitive elements such as the accelerometer in the integrated navigation system, gyroscope, geomagnetic sensor, zero meeting such as inclined to one side change with environmental change; Especially receive Influence of Temperature bigger, therefore no longer reliable under the resulting constant multiplier of indoor standardization, zero parameter lowered in field environment such as inclined to one side; For protecting the precision of positive integrated navigation system; Tackling the constant multiplier, zero of each sensor revises partially; But owing to there is not calibration facility such as turntable under the environment such as field, therefore can't the constant multiplier, zero of each sensor be revised partially, reduced the measuring accuracy of each sensor.

Summary of the invention

The object of the invention is exactly the problem that exists to above-mentioned prior art; A kind of open-air scaling method of under the situation of calibration facilities such as no turntable, inertial sensors such as accelerometer, geomagnetic sensor and gyroscope being demarcated is provided, reaches the purpose that improves the sensor measurement precision.

The objective of the invention is to realize like this, open-air scaling method step is:

At first provide accelerometer, geomagnetic sensor and gyrostatic measurement model in the minitype combined navigation system, analyze the main error component of field environment lower sensor; Adopt a kind of six location position method of combination then, through the solving equation group, to obtain accelerometer, geomagnetic sensor and gyrostatic constant multiplier, zero correction factor partially; Concrete operations are following:

(1) the open-air scaling method of accelerometer

When indoor standardization, the measurement model of general accelerometer does

$\left\{\begin{array}{c}{a}_x=(b_x+n_{\mathrm{ax}}+E_{\mathrm{xy}}{n}_{\mathrm{ay}}+E_{\mathrm{xz}}{n}_{\mathrm{az}})/k_x\\ a_y=(b_y+E_{\mathrm{yx}}{n}_{\mathrm{ax}}+n_{\mathrm{ay}}+E_{\mathrm{yz}}{n}_{\mathrm{az}})/k_y\\ a_z=(b_z+E_{\mathrm{zx}}{n}_{\mathrm{ax}}+E_{\mathrm{zy}}{n}_{\mathrm{ay}}+n_{\mathrm{az}})/k_z\end{array}\right.---\left(1\right)$

In the formula, a _x, a _y, a _zBe respectively the acceleration after the compensation of X, Y, three axis accelerometers of Z, unit is m/s ²

n _Ax, n _Ay, n _AzBe respectively the measured value of the not compensated of X, Y, three axis accelerometers of Z, unit is voltage volt or umber of pulse;

b _x, b _y, b _zBe respectively X, Y, Z accelerometer zero partially, unit is voltage volt or umber of pulse;

k _x, k _y, k _zBe respectively the constant multiplier of X, Y, Z accelerometer, unit is V/ (m/s ²);

E _Xy, E _Xz, E _Yx, E _Yz, E _Zx, E _ZyBe respectively the alignment error of three axis accelerometers;

Through speed trial and position test, the constant multiplier, zero that records accelerometer partially and parameter such as alignment error,

Under the lowered in field environment, when Inertial Measurement Unit was static, that responsive was local gravitational acceleration G to accelerometer ₀(≈ 9.8m/s ²), therefore have:

$a_x^2+a_y^2+a_z^2=G_0^2---\left(2\right)$

Receive the interference of factors such as temperature, accelerometer zero partially, bigger variation can take place in constant multiplier etc., but that its alignment error changes is very little; Can ignore; Think that the alignment error angle that indoor standardization obtains remains valid, therefore, the correction model of accelerometer is expressed as:

$\left\{\begin{array}{c}{A}_x=B_x+K_x{a}_x\\ A_y=B_y+K_y{a}_y\\ A_z=B_z+K_z{a}_z\end{array}\right.---\left(3\right)$

In the formula, A _x, A _y, A _zBe the value after the acceleration correction of X, Y, Z accelerometer measures under the field environment, unit is m/s ²

B _x, B _y, B _zBe respectively zero inclined to one side modified value of X under the field environment, Y, Z accelerometer;

K _x, K _y, K _zBe respectively the constant multiplier modified value of X under the field environment, Y, Z accelerometer;

When Inertial Measurement Unit uses in the open air, rotate 6 different orientation, after static a period of time, can obtain the state equation of six positions by (2), (3) formula:

${(K_x{a}_{x1}+B_x)}^2+{(K_y{a}_{y1}+B_y)}^2+{(K_z{a}_{z1}+B_z)}^2=G_0^2---\left(4\right)$

${(K_x{a}_{x2}+B_x)}^2+{(K_y{a}_{y2}+B_y)}^2+{(K_z{a}_{z2}+B_z)}^2=G_0^2---\left(5\right)$

${(K_x{a}_{x3}+B_x)}^2+{(K_y{a}_{y3}+B_y)}^2+{(K_z{a}_{z3}+B_z)}^2=G_0^2---\left(6\right)$

${(K_x{a}_{x4}+B_x)}^2+{(K_y{a}_{y4}+B_y)}^2+{(K_z{a}_{z4}+B_z)}^2=G_0^2---\left(7\right)$

${(K_x{a}_{x5}+B_x)}^2+{(K_y{a}_{y5}+B_y)}^2+{(K_z{a}_{z5}+B_z)}^2=G_0^2---\left(8\right)$

${(K_x{a}_{x6}+B_x)}^2+{(K_y{a}_{y6}+B_y)}^2+{(K_z{a}_{z6}+B_z)}^2=G_0^2---\left(9\right)$

Get by formula (5)-(4), (6)-(5), (7)-(6), (8)-(7), (9)-(8):

$K_x^2(a_{x2}^2-a_{x1}^2)+2K_x{B}_x+(a_{x2}-a_{x1})+K_y^2(a_{y2}^2-a_{y1}^2)+$

$2K_y{B}_y(a_{y2}-a_{y1})+K_z^2(a_{z2}^2-a_{z1}^2)+2K_z{B}_z(a_{z2}-a_{z1})=0---\left(10\right)$

$K_x^2(a_{x3}^2-a_{x2}^2)+2K_x{B}_x(a_{x3}-a_{x2})+K_y^2(a_{y3}^2-a_{y2}^2)+$

$2K_y{B}_y(a_{y3}-a_{y3})+K_z^2(a_{z3}^2-a_{z2}^2)+2K_z{B}_z(a_{z3}-a_{z2})=0---\left(11\right)$

$K_x^2(a_{x4}^2-a_{x3}^2)+2K_x{B}_x(a_{x4}-a_{x3})+K_y^2(a_{y4}^2-a_{y3}^2)+$

$2K_y{B}_y(a_{y4}-a_{y3})+K_z^2(a_{z4}^2-a_{z3}^2)+2K_z{B}_z(a_{z4}-a_{z3})=0---\left(12\right)$

$K_x^2(a_{x5}^2-a_{x4}^2)+2K_x{B}_x(a_{x5}-a_{x4})+K_y^2(a_{y5}^2-a_{y4}^2)+$

$2K_y{B}_y(a_{y5}-a_{y4})+K_z^2(a_{z5}^2-a_{z4}^2)+2K_z{B}_z(a_{z5}-a_{z4})=0---\left(13\right)$

$K_x^2(a_{x6}^2-a_{x5}^2)+2K_x{B}_x(a_{x6}-a_{x5})+K_y^2(a_{y6}^2-a_{y5}^2)+$

$2K_y{B}_y(a_{y6}-a_{y5})+K_z^2(a_{z6}^2-a_{z5}^2)+2K_z{B}_z(a_{z6}-a_{z5})=0---\left(14\right)$

First on the equality left side is moved to the right, and gets divided by

simultaneously:

$2K_x{B}_x(a_{x2}-a_{x1})/K_x^2+K_y^2(a_{y2}^2-a_{y1}^2)/K_x^2+2K_y{B}_y(a_{y2}-a_{y1})/K_x^2+$

$K_z^2(a_{z2}^2-a_{z1}^2)/K_x^2+{2K}_z{B}_z(a_{z2}-a_{z1})/K_x^2=a_{x1}^2-a_{x2}^2---\left(15\right)$

$2K_x{B}_x(a_{x3}-a_{x2})/K_x^2+K_y^2(a_{y3}^2-a_{y2}^2)/K_x^2+2K_y{B}_y(a_{y3}-a_{y3})/K_x^2+$

$K_z^2(a_{z3}^2-a_{z2}^2)/K_x^2+{2K}_z{B}_z(a_{z3}-a_{z2})/K_x^2=a_{x2}^2-a_{x3}^2---\left(16\right)$

$2K_x{B}_x(a_{x4}-a_{x3})/K_x^2+K_y^2(a_{y4}^2-a_{y3}^2)/K_x^2+2K_y{B}_y(a_{y4}-a_{y3})/K_x^2+$

$K_z^2(a_{z4}^2-a_{z3}^2)/K_x^2+{2K}_z{B}_z(a_{z4}-a_{z3})/K_x^2=a_{x3}^2-a_{x4}^2---\left(17\right)$

$2K_x{B}_x(a_{x5}-a_{x4})/K_x^2+K_y^2(a_{y5}^2-a_{y4}^2)/K_x^2+2K_y{B}_y(a_{y5}-a_{y4})/K_x^2+$

$K_z^2(a_{z5}^2-a_{z4}^2)/K_x^2+{2K}_z{B}_z(a_{z5}-a_{z4})/K_x^2=a_{x4}^2-a_{x5}^2---\left(18\right)$

$2K_x{B}_x(a_{x6}-a_{x5})/K_x^2+K_y^2(a_{y6}^2-a_{y5}^2)/K_x^2+2K_y{B}_y(a_{y6}-a_{y5})/K_x^2+$

$K_z^2(a_{z6}^2-a_{z5}^2)/K_x^2+{2K}_z{B}_z(a_{z6}-a_{z5})/K_x^2=a_{x5}^2-a_{x6}^2---\left(19\right)$

It is rewritten as matrix form is:

$\left[\begin{array}{ccccc}2(a_{x2}-a_{x1})& a_{y2}^2-a_{y1}^2& 2(a_{y2}-a_{y1})& a_{z2}^2-a_{z1}^2& 2(a_{z2}-a_{z1})\\ 2(a_{x3}-a_{x2})& a_{y3}^2-a_{y2}^2& 2(a_{y3}-a_{y2})& a_{z3}^2-a_{z2}^2& 2(a_{z3}-a_{z2})\\ 2(a_{x4}-a_{x3})& a_{y4}^2-a_{y3}^2& 2(a_{y4}-a_{y3})& a_{z4}^2-a_{z3}^2& 2(a_{z4}-a_{z3})\\ 2(a_{x5}-a_{x4})& a_{y5}^2-a_{y4}^2& 2(a_{y5}-a_{y4})& a_{z5}^2-a_{z4}^2& 2(a_{z5}-a_{z4})\\ 2(a_{x6}-a_{x5})& a_{y6}^2-a_{y5}^2& 2(a_{y6}-a_{y5})& a_{z6}^2-a_{z5}^2& 2(a_{z6}-z_{z5})\end{array}\right]\left[\begin{array}{c}{K}_x{B}_x/K_x^2\\ K_y^2/K_x^2\\ K_y{B}_y/K_x^2\\ K_z^2/K_x^2\\ K_z{B}_z/K_x^2\end{array}\right]=\left[\begin{array}{c}{a}_{x1}^2-a_{x2}^2\\ a_{x2}^2-a_{x3}^2\\ a_{x3}^2-a_{x4}^2\\ a_{x4}^2-a_{x5}^2\\ a_{x5}^2-a_{x6}^2\end{array}\right]---\left(20\right)$

It is expressed as:

M×C＝F (21)

In the following formula, matrix M is a given value, forms C=[C by the measured value of the accelerometer of 6 positions ₁, C ₂, C ₃, C ₄, C ₅] being parameter to be asked, F also is a given value, therefore, C=M ^-1F, like this,

$\left\{\begin{array}{c}{K}_x{B}_x/K_x^2=C_1\\ K_y^2/K_x^2=C_2\\ K_y{B}_y/K_x^2=C_3\\ K_z^2/K_x^2=C_4\\ K_z{B}_z/K_x^2=C_5\end{array}\right.---\left(22\right)$

Can know by (22):

$\left\{\begin{array}{c}{B}_x=C_1{K}_x\\ K_y=\sqrt{C_2{K}_x^2}\\ B_y=C_3{K}_x^2/\sqrt{C_2{K}_x^2}\\ K_z=\sqrt{C_4{K}_x^2}\\ B_z=C_5{K}_x^2/\sqrt{C_4{K}_x^2}\end{array}\right.---\left(23\right)$

Formula (23) back substitution is gone in the formula (4) and can be got:

${(K_x{A}_{x1}+C_1{K}_x)}^2+{(A_{y1}\sqrt{C_2{K}_x^2}+C_3{K}_x^2/\sqrt{C_2{K}_x^2})}^2+{(A_{z1}\sqrt{C_4{K}_x^2}+C_5{K}_x^2/\sqrt{C_4{K}_x^2})}^2=G_0^2---\left(24\right)$

Can get thus: $K_x=G_0/\sqrt{A_{x1}^2+2C_1{A}_{x1}+C_1^2+C_2{A}_{y1}^2+2C_3{A}_{y1}+C_3^2/C_2+C_4{A}_{z1}^2+{C_5}^2/C_4+2C_5{A}_{z1}}---\left(25\right)$

With formula (25) substitution formula (23), can obtain K successively _y, K _z, B _x, B _y, B _zValue, accomplish accelerometer zero partially with the open-air demarcation of constant multiplier;

(2) the open-air scaling method of geomagnetic sensor

Calibration principle is identical with accelerometer with model under the geomagnetic sensor lowered in field environment, and scaling method is with the open-air scaling method of above-mentioned accelerometer;

(3) the open-air scaling method of gyroscope

Because it is the gyroscope survey noise is bigger, responsive less than rotational-angular velocity of the earth (ω _Ie=15.0411 °/h), its output is about zero, and therefore, gyrostatic output can regard that it is partially zero as during position 1; In like manner, gyrostatic output valve can regard that all it zero partially as when position 2, position 3, position 4, position 5, position 6; Accurate for further, it is partially zero as it the gyrostatic output of 6 positions to be averaged.

The sensor that major advantage of the present invention is to demarcate in the integrated navigation system does not need reference device such as turntable; Be specially adapted to the field work requirement; This scaling method is with low cost, effectively simple, only needs can accomplish demarcation through rotating six different positions; Precision is high, usable range is wide, can be in the field widespread uses such as outdoor navigation of unmanned plane, underwater hiding-machine, automobile,

Description of drawings

Fig. 1 is open-air six position views of demarcating of minitype combined navigation system

Fig. 2 is the open-air scaling method process flow diagram of minitype combined navigation system

Embodiment

Below in conjunction with accompanying drawing embodiment of the present invention is described in detail,

Said open-air scaling method step is: at first provide accelerometer in the integrated navigation system, geomagnetic sensor and gyrostatic measurement model, analyze the main error component of each sensor under the field environment; Adopt a kind of six location position method of combination then, through the solving equation group, to obtain accelerometer, geomagnetic sensor and gyrostatic constant multiplier, zero correction factor partially; Its concrete operations are following:

(1) the open-air scaling method of accelerometer

When indoor standardization, the measurement model of general accelerometer does

$\left\{\begin{array}{c}{a}_x=(b_x+n_{\mathrm{ax}}+E_{\mathrm{xy}}{n}_{\mathrm{ay}}+E_{\mathrm{xz}}{n}_{\mathrm{az}})/k_x\\ a_y=(b_y+E_{\mathrm{yx}}{n}_{\mathrm{ax}}+n_{\mathrm{ay}}+E_{\mathrm{yz}}{n}_{\mathrm{az}})/k_y\\ a_z=(b_z+E_{\mathrm{zx}}{n}_{\mathrm{ax}}+E_{\mathrm{zy}}{n}_{\mathrm{ay}}+n_{\mathrm{az}})/k_z\end{array}\right.---\left(1\right)$

In the formula, a _x, a _y, a _zBe respectively the acceleration after the compensation of X, Y, three axis accelerometers of Z, unit is m/s ²

n _Ax, n _Ay, n _AzBe respectively the measured value of the not compensated of X, Y, three axis accelerometers of Z, unit is voltage volt or umber of pulse;

b _x, b _y, b _zBe respectively X, Y, Z accelerometer zero partially, unit is voltage volt or umber of pulse;

k _x, k _y, k _zBe respectively the constant multiplier of X, Y, Z accelerometer, unit is V/ (m/s ²);

E _Xy, E _Xz, E _Yx, E _Yz, E _Zx, E _ZyBe respectively the alignment error of three axis accelerometers;

Through speed trial and position test, the constant multiplier, zero that records accelerometer partially and parameter such as alignment error;

Under the lowered in field environment, when Inertial Measurement Unit was static in the integrated navigation system, that responsive was local gravitational acceleration G to accelerometer ₀(≈ 9.8m/s ²), have:

$a_x^2+a_y^2+a_z^2=G_0^2---\left(2\right)$

Therefore, the correction model of accelerometer is expressed as: $\left\{\begin{array}{c}{A}_x=B_x+K_x{a}_x\\ A_y=B_y+K_y{a}_y\\ A_z=B_z+K_z{a}_z\end{array}\right.---\left(3\right)$

In the formula, A _z, A _y, A _zBe the value after the acceleration correction of X, Y, Z accelerometer measures under the field environment, unit is m/s ²

B _x, B _y, B _zBe respectively zero inclined to one side modified value of X under the field environment, Y, Z accelerometer;

K _x, K _y, K _zBe respectively the constant multiplier modified value of X under the field environment, Y, Z accelerometer;

When Inertial Measurement Unit uses in the open air, rotate 6 different orientation, after static a period of time, can obtain the state equation of six positions by (2), (3) formula:

${(K_x{a}_{x1}+B_x)}^2+{(K_y{a}_{y1}+B_y)}^2+{(K_z{a}_{z1}+B_z)}^2=G_0^2---\left(4\right)$

${(K_x{a}_{x2}+B_x)}^2+{(K_y{a}_{y2}+B_y)}^2+{(K_z{a}_{z2}+B_z)}^2=G_0^2---\left(5\right)$

${(K_x{a}_{x3}+B_x)}^2+{(K_y{a}_{y3}+B_y)}^2+{(K_z{a}_{z3}+B_z)}^2=G_0^2---\left(6\right)$

${(K_x{a}_{x4}+B_x)}^2+{(K_y{a}_{y4}+B_y)}^2+{(K_z{a}_{z4}+B_z)}^2=G_0^2---\left(7\right)$

${(K_x{a}_{x5}+B_x)}^2+{(K_y{a}_{y5}+B_y)}^2+{(K_z{a}_{z5}+B_z)}^2=G_0^2---\left(8\right)$

${(K_x{a}_{x6}+B_x)}^2+{(K_y{a}_{y6}+B_y)}^2+{(K_z{a}_{z6}+B_z)}^2=G_0^2---\left(9\right)$

Get by formula (5)-(4), (6)-(5), (7)-(6), (8)-(7), (9)-(8):

$K_x^2(a_{x2}^2-a_{x1}^2)+2K_x{B}_x+(a_{x2}-a_{x1})+K_y^2(a_{y2}^2-a_{y1}^2)+$

$2K_y{B}_y(a_{y2}-a_{y1})+K_z^2(a_{z2}^2-a_{z1}^2)+2K_z{B}_z(a_{z2}-a_{z1})=0---\left(10\right)$

$K_x^2(a_{x3}^2-a_{x2}^2)+2K_x{B}_x(a_{x3}-a_{x2})+K_y^2(a_{y3}^2-a_{y2}^2)+$

$2K_y{B}_y(a_{y3}-a_{y3})+K_z^2(a_{z3}^2-a_{z2}^2)+2K_z{B}_z(a_{z3}-a_{z2})=0---\left(11\right)$

$K_x^2(a_{x4}^2-a_{x3}^2)+2K_x{B}_x(a_{x4}-a_{x3})+K_y^2(a_{y4}^2-a_{y3}^2)+$

$2K_y{B}_y(a_{y4}-a_{y3})+K_z^2(a_{z4}^2-a_{z3}^2)+2K_z{B}_z(a_{z4}-a_{z3})=0---\left(12\right)$

$K_x^2(a_{x5}^2-a_{x4}^2)+2K_x{B}_x(a_{x5}-a_{x4})+K_y^2(a_{y5}^2-a_{y4}^2)+$

$2K_y{B}_y(a_{y5}-a_{y4})+K_z^2(a_{z5}^2-a_{z4}^2)+2K_z{B}_z(a_{z5}-a_{z4})=0---\left(13\right)$

$K_x^2(a_{x6}^2-a_{x5}^2)+2K_x{B}_x(a_{x6}-a_{x5})+K_y^2(a_{y6}^2-a_{y5}^2)+$

$2K_y{B}_y(a_{y6}-a_{y5})+K_z^2(a_{z6}^2-a_{z5}^2)+2K_z{B}_z(a_{z6}-a_{z5})=0---\left(14\right)$

First on the equality left side is moved to the right, and gets divided by

simultaneously:

$2K_x{B}_x(a_{x2}-a_{x1})/K_x^2+K_y^2(a_{y2}^2-a_{y1}^2)/K_x^2+2K_y{B}_y(a_{y2}-a_{y1})/K_x^2+$

$K_z^2(a_{z2}^2-a_{z1}^2)/K_x^2+{2K}_z{B}_z(a_{z2}-a_{z1})/K_x^2=a_{x1}^2-a_{x2}^2---\left(15\right)$

$2K_x{B}_x(a_{x3}-a_{x2})/K_x^2+K_y^2(a_{y3}^2-a_{y2}^2)/K_x^2+2K_y{B}_y(a_{y3}-a_{y3})/K_x^2+$

$K_z^2(a_{z3}^2-a_{z2}^2)/K_x^2+{2K}_z{B}_z(a_{z3}-a_{z2})/K_x^2=a_{x2}^2-a_{x3}^2---\left(16\right)$

$2K_x{B}_x(a_{x4}-a_{x3})/K_x^2+K_y^2(a_{y4}^2-a_{y3}^2)/K_x^2+2K_y{B}_y(a_{y4}-a_{y3})/K_x^2+$

$K_z^2(a_{z4}^2-a_{z3}^2)/K_x^2+{2K}_z{B}_z(a_{z4}-a_{z3})/K_x^2=a_{x3}^2-a_{x4}^2---\left(17\right)$

$2K_x{B}_x(a_{x5}-a_{x4})/K_x^2+K_y^2(a_{y5}^2-a_{y4}^2)/K_x^2+2K_y{B}_y(a_{y5}-a_{y4})/K_x^2+$

$K_z^2(a_{z5}^2-a_{z4}^2)/K_x^2+{2K}_z{B}_z(a_{z5}-a_{z4})/K_x^2=a_{x4}^2-a_{x5}^2---\left(18\right)$

$2K_x{B}_x(a_{x6}-a_{x5})/K_x^2+K_y^2(a_{y6}^2-a_{y5}^2)/K_x^2+2K_y{B}_y(a_{y6}-a_{y5})/K_x^2+$

$K_z^2(a_{z6}^2-a_{z5}^2)/K_x^2+{2K}_z{B}_z(a_{z6}-a_{z5})/K_x^2=a_{x5}^2-a_{x6}^2---\left(19\right)$

It is rewritten as matrix form is:

It is expressed as:

M×C＝F (21)

In the following formula, matrix M is a given value, forms C=[C by the measured value of the accelerometer of 6 positions ₁, C ₂, C ₃, C ₄, C ₅] being parameter to be asked, F also is a given value, therefore, C=M ^-1F, like this,

$\left\{\begin{array}{c}{K}_x{B}_x/K_x^2=C_1\\ K_y^2/K_x^2=C_2\\ K_y{B}_y/K_x^2=C_3\\ K_z^2/K_x^2=C_4\\ K_z{B}_z/K_x^2=C_5\end{array}\right.---\left(22\right)$

Can know by (22):

$\left\{\begin{array}{c}{B}_x=C_1{K}_x\\ K_y=\sqrt{C_2{K}_x^2}\\ B_y=C_3{K}_x^2/\sqrt{C_2{K}_x^2}\\ K_z=\sqrt{C_4{K}_x^2}\\ B_z=C_5{K}_x^2/\sqrt{C_4{K}_x^2}\end{array}\right.---\left(23\right)$

Formula (23) back substitution is gone in the formula (4) and can be got:

${(K_x{A}_{x1}+C_1{K}_x)}^2+{(A_{y1}\sqrt{C_2{K}_x^2}+C_3{K}_x^2/\sqrt{C_2{K}_x^2})}^2+{(A_{z1}\sqrt{C_4{K}_x^2}+C_5{K}_x^2/\sqrt{C_4{K}_x^2})}^2=G_0^2---\left(24\right)$

Can get thus:

$K_x=G_0/\sqrt{A_{x1}^2+2C_1{A}_{x1}+C_1^2+C_2{A}_{y1}^2+2C_3{A}_{y1}+C_3^2/C_2+C_4{A}_{z1}^2+{C_5}^2/C_4+2C_5{A}_{z1}}---\left(25\right)$

With formula (25) substitution formula (23), can obtain K successively _y, K _z, B _x, B _y, B _zValue, accomplish accelerometer zero partially with the open-air demarcation of constant multiplier;

(2) the open-air scaling method of geomagnetic sensor

Calibration principle is identical with accelerometer with model under the geomagnetic sensor lowered in field environment, and scaling method is with the open-air scaling method of above-mentioned accelerometer;

(3) the open-air scaling method of gyroscope

Because it is the gyroscope survey noise is bigger, responsive less than rotational-angular velocity of the earth (ω _Ie=15.0411 °/h), its output is about zero, therefore; Adopt six location position layouts; Gyrostatic output can regard that it is partially zero as during position 1, and in like manner, gyrostatic output valve can regard that all it is partially zero as when position 2, position 3, position 4, position 5, position 6; Accurate for further, it is partially zero as it the gyrostatic output of 6 positions to be averaged,

Open-air timing signal; Integrated navigation system is positioned over ground with any attitude; Keep static a period of time, rotate 5 times then, note accelerometer, geomagnetic sensor and the gyroscope output valve of each position to obtain 6 positions; Calculate substitution formula (4)～(25), can obtain zero inclined to one side, the isoparametric modified value of constant multiplier under each sensitive element lowered in field environment in the navigational system.

Claims (1)

1. the open-air scaling method of the sensor in the minitype combined navigation system; It is characterized in that said open-air scaling method step is: at first provide accelerometer in the integrated navigation system, geomagnetic sensor and gyrostatic measurement model, analyze the main error component of each sensor under the field environment; Adopt a kind of six location position method of combination then, through the solving equation group, to obtain accelerometer, geomagnetic sensor and gyrostatic constant multiplier, zero correction factor partially; Its concrete operations are following:

(1) the open-air scaling method of accelerometer

When indoor standardization, the measurement model of general accelerometer does

$\left\{\begin{array}{c}{a}_x=(b_x+n_{\mathrm{ax}}+E_{\mathrm{xy}}{n}_{\mathrm{ay}}+E_{\mathrm{xz}}{n}_{\mathrm{az}})/k_x\\ a_y=(b_y+E_{\mathrm{yx}}{n}_{\mathrm{ax}}+n_{\mathrm{ay}}+E_{\mathrm{yz}}{n}_{\mathrm{az}})/k_y\\ a_z=(b_z+E_{\mathrm{zx}}{n}_{\mathrm{ax}}+E_{\mathrm{zy}}{n}_{\mathrm{ay}}+n_{\mathrm{az}})/k_z\end{array}\right.---\left(1\right)$

In the formula, a _x, a _y, a _zBe respectively the acceleration after the compensation of X, Y, three axis accelerometers of Z, unit is m/s ²

n _Ax, n _Ay, n _AzBe respectively the measured value of the not compensated of X, Y, three axis accelerometers of Z, unit is voltage volt or umber of pulse;

b _x, b _y, b _zBe respectively X, Y, Z accelerometer zero partially, unit is voltage volt or umber of pulse;

k _x, k _y, k _zBe respectively the constant multiplier of X, Y, Z accelerometer, unit is V/ (m/s ²);

E _Xy, E _Xz, E _Yx, E _Yz, E _Zx, E _ZyBe respectively the alignment error of three axis accelerometers;

Through speed trial and position test, the constant multiplier, zero that records accelerometer partially and parameter such as alignment error;

Under the lowered in field environment, when Inertial Measurement Unit was static in the integrated navigation system, that responsive was local gravitational acceleration G to accelerometer ₀(≈ 9.8m/s ²), have:

$a_x^2+a_y^2+a_z^2=G_0^2---\left(2\right)$

Therefore, the correction model of accelerometer is expressed as:

$\left\{\begin{array}{c}{A}_x=B_x+K_x{a}_x\\ A_y=B_y+K_y{a}_y\\ A_z=B_z+K_z{a}_z\end{array}\right.---\left(3\right)$

In the formula, A _x, A _y, A _zBe the value after the acceleration correction of X, Y, Z accelerometer measures under the field environment, unit is m/s ²

B _x, B _y, B _zBe respectively zero inclined to one side modified value of X under the field environment, Y, Z accelerometer;

K _x, K _y, K _zBe respectively the constant multiplier modified value of X under the field environment, Y, Z accelerometer;

When Inertial Measurement Unit uses in the open air, rotate 6 different orientation, after static a period of time, can obtain the state equation of six positions by (2), (3) formula:

${(K_x{a}_{x1}+B_x)}^2+{(K_y{a}_{y1}+B_y)}^2+{(K_z{a}_{z1}+B_z)}^2=G_0^2---\left(4\right)$

${(K_x{a}_{x2}+B_x)}^2+{(K_y{a}_{y2}+B_y)}^2+{(K_z{a}_{z2}+B_z)}^2=G_0^2---\left(5\right)$

${(K_x{a}_{x3}+B_x)}^2+{(K_y{a}_{y3}+B_y)}^2+{(K_z{a}_{z3}+B_z)}^2=G_0^2---\left(6\right)$

${(K_x{a}_{x4}+B_x)}^2+{(K_y{a}_{y4}+B_y)}^2+{(K_z{a}_{z4}+B_z)}^2=G_0^2---\left(7\right)$

${(K_x{a}_{x5}+B_x)}^2+{(K_y{a}_{y5}+B_y)}^2+{(K_z{a}_{z5}+B_z)}^2=G_0^2---\left(8\right)$

${(K_x{a}_{x6}+B_x)}^2+{(K_y{a}_{y6}+B_y)}^2+{(K_z{a}_{z6}+B_z)}^2=G_0^2---\left(9\right)$

Get by formula (5)-(4), (6)-(5), (7)-(6), (8)-(7), (9)-(8):

$K_x^2(a_{x2}^2-a_{x1}^2)+2K_x{B}_x+(a_{x2}-a_{x1})+K_y^2(a_{y2}^2-a_{y1}^2)+$

$2K_y{B}_y(a_{y2}-a_{y1})+K_z^2(a_{z2}^2-a_{z1}^2)+2K_z{B}_z(a_{z2}-a_{z1})=0---\left(10\right)$

$K_x^2(a_{x3}^2-a_{x2}^2)+2K_x{B}_x(a_{x3}-a_{x2})+K_y^2(a_{y3}^2-a_{y2}^2)+$

$2K_y{B}_y(a_{y3}-a_{y3})+K_z^2(a_{z3}^2-a_{z2}^2)+2K_z{B}_z(a_{z3}-a_{z2})=0---\left(11\right)$

$K_x^2(a_{x4}^2-a_{x3}^2)+2K_x{B}_x(a_{x4}-a_{x3})+K_y^2(a_{y4}^2-a_{y3}^2)+$

$2K_y{B}_y(a_{y4}-a_{y3})+K_z^2(a_{z4}^2-a_{z3}^2)+2K_z{B}_z(a_{z4}-a_{z3})=0---\left(12\right)$

$K_x^2(a_{x5}^2-a_{x4}^2)+2K_x{B}_x(a_{x5}-a_{x4})+K_y^2(a_{y5}^2-a_{y4}^2)+$

$2K_y{B}_y(a_{y5}-a_{y4})+K_z^2(a_{z5}^2-a_{z4}^2)+2K_z{B}_z(a_{z5}-a_{z4})=0---\left(13\right)$

$K_x^2(a_{x6}^2-a_{x5}^2)+2K_x{B}_x(a_{x6}-a_{x5})+K_y^2(a_{y6}^2-a_{y5}^2)+$

$2K_y{B}_y(a_{y6}-a_{y5})+K_z^2(a_{z6}^2-a_{z5}^2)+2K_z{B}_z(a_{z6}-a_{z5})=0---\left(14\right)$

First on the equality left side is moved to the right, and gets divided by

simultaneously:

$2K_x{B}_x(a_{x2}-a_{x1})/K_x^2+K_y^2(a_{y2}^2-a_{y1}^2)/K_x^2+2K_y{B}_y(a_{y2}-a_{y1})/K_x^2+$

$K_z^2(a_{z2}^2-a_{z1}^2)/K_x^2+{2K}_z{B}_z(a_{z2}-a_{z1})/K_x^2=a_{x1}^2-a_{x2}^2---\left(15\right)$

$2K_x{B}_x(a_{x3}-a_{x2})/K_x^2+K_y^2(a_{y3}^2-a_{y2}^2)/K_x^2+2K_y{B}_y(a_{y3}-a_{y3})/K_x^2+$

$K_z^2(a_{z3}^2-a_{z2}^2)/K_x^2+{2K}_z{B}_z(a_{z3}-a_{z2})/K_x^2=a_{x2}^2-a_{x3}^2---\left(16\right)$

$2K_x{B}_x(a_{x4}-a_{x3})/K_x^2+K_y^2(a_{y4}^2-a_{y3}^2)/K_x^2+2K_y{B}_y(a_{y4}-a_{y3})/K_x^2+$

$K_z^2(a_{z4}^2-a_{z3}^2)/K_x^2+{2K}_z{B}_z(a_{z4}-a_{z3})/K_x^2=a_{x3}^2-a_{x4}^2---\left(17\right)$

$2K_x{B}_x(a_{x5}-a_{x4})/K_x^2+K_y^2(a_{y5}^2-a_{y4}^2)/K_x^2+2K_y{B}_y(a_{y5}-a_{y4})/K_x^2+$

$K_z^2(a_{z5}^2-a_{z4}^2)/K_x^2+{2K}_z{B}_z(a_{z5}-a_{z4})/K_x^2=a_{x4}^2-a_{x5}^2---\left(18\right)$

$2K_x{B}_x(a_{x6}-a_{x5})/K_x^2+K_y^2(a_{y6}^2-a_{y5}^2)/K_x^2+2K_y{B}_y(a_{y6}-a_{y5})/K_x^2+$

$K_z^2(a_{z6}^2-a_{z5}^2)/K_x^2+{2K}_z{B}_z(a_{z6}-a_{z5})/K_x^2=a_{x5}^2-a_{x6}^2---\left(19\right)$

It is rewritten as matrix form is:

It is expressed as:

M×C＝F (21)

In the following formula, matrix M is a given value, forms C=[C by the measured value of the accelerometer of 6 positions ₁, C ₂, C ₃, C ₄, C ₅] being parameter to be asked, F also is a given value, therefore, C=M ^-1F, like this,

$\left\{\begin{array}{c}{K}_x{B}_x/K_x^2=C_1\\ K_y^2/K_x^2=C_2\\ K_y{B}_y/K_x^2=C_3\\ K_z^2/K_x^2=C_4\\ K_z{B}_z/K_x^2=C_5\end{array}\right.---\left(22\right)$

Can know by (22):

$\left\{\begin{array}{c}{B}_x=C_1{K}_x\\ K_y=\sqrt{C_2{K}_x^2}\\ B_y=C_3{K}_x^2/\sqrt{C_2{K}_x^2}\\ K_z=\sqrt{C_4{K}_x^2}\\ B_z=C_5{K}_x^2/\sqrt{C_4{K}_x^2}\end{array}\right.---\left(23\right)$

Formula (23) back substitution is gone in the formula (4) and can be got:

${(K_x{A}_{x1}+C_1{K}_x)}^2+{(A_{y1}\sqrt{C_2{K}_x^2}+C_3{K}_x^2/\sqrt{C_2{K}_x^2})}^2+{(A_{z1}\sqrt{C_4{K}_x^2}+C_5{K}_x^2/\sqrt{C_4{K}_x^2})}^2=G_0^2---\left(24\right)$

Can get thus:

$K_x=G_0/\sqrt{A_{x1}^2+2C_1{A}_{x1}+C_1^2+C_2{A}_{y1}^2+2C_3{A}_{y1}+C_3^2/C_2+C_4{A}_{z1}^2+{C_5}^2/C_4+2C_5{A}_{z1}}---\left(25\right)$

With formula (25) substitution formula (23), can obtain K successively _y, K _z, B _x, B _y, B _zValue, accomplish accelerometer zero partially with the open-air demarcation of constant multiplier;

(2) the open-air scaling method of geomagnetic sensor

Calibration principle is identical with accelerometer with model under the geomagnetic sensor lowered in field environment, and scaling method is with the open-air scaling method of above-mentioned accelerometer;

(3) the open-air scaling method of gyroscope

The gyroscope sensitivity is less than rotational-angular velocity of the earth (ω _Ie=15.0411 °/h), its output is about zero, adopts six location position layouts, and gyrostatic output can regard that it is partially zero as during position 1, and in like manner, gyrostatic output valve can regard that all it is partially zero as when position 2, position 3, position 4, position 5, position 6; Accurate for further, it is partially zero as it the gyrostatic output of 6 positions to be averaged.

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