CN108037318A - A kind of unmanned plane accelerometer calibration method based on ellipsoid fitting - Google Patents
A kind of unmanned plane accelerometer calibration method based on ellipsoid fitting Download PDFInfo
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Abstract
The invention belongs to unmanned air vehicle technique field, discloses a kind of unmanned plane accelerometer calibration method based on ellipsoid fitting.Random-Rotation unmanned plane, makes its posture position span cover the three dimensions scope where fitting spheroid as far as possible, a series of output valve of accelerometer in the case where each test position stationary acquisition obtains different postures；Ellipsoidal Surface is fitted by the accelerometer output valve measured；Calibration factor is obtained by the Ellipsoidal Surface fitted；Compensated using the output of calibration parameter and calibrating patterns to unmanned plane accelerometer.The present invention being capable of the quickly and accurately null offset of calibrating accolerometer and calibration factor；Independent of large-scale precision equipment, only multiple and different postures need to be positioned over by accelerometer is static；Calculation amount is small, and arithmetic speed is fast, can be rapidly completed calibration, has certain engineering application value.The method of the present invention is easy to operate, quickly calibrated suitable for the unmanned plane accelerometer of most occasions independent of external device.
Description
Technical field
The invention belongs to unmanned air vehicle technique field, more particularly to a kind of unmanned plane accelerometer calibration based on ellipsoid fitting
Method.
Background technology
Accelerometer is an indispensable sensor for unmanned plane.It provides nobody for flight control system
The attitude information of machine so that unmanned plane can carry out navigational guidance and control.But accelerometer is being produced, installing and measured
Certain error can be inevitably produced in journey, in order to ensure the accuracy of accelerometer measures data, need before the use pair plus
Speedometer is calibrated.Existing accelerometer calibration method is generally dependent upon high-precision turntable.But turntable there is
The features such as quality and volume are big, not easily shifted and equipment is expensive.It is this easy to carry for unmanned plane, in a variety of contexts
For using flexible aircraft, calibrating accolerometer can not be carried out using turntable under many circumstances.There can only be turntable in advance
Local calibration in advance, whether then no matter using area changes, is all no longer calibrated.For the changeable unmanned plane of using area
For, it is evident that it can so produce calibration error.
In conclusion problem existing in the prior art is：There are turntable quality and body for existing accelerometer calibration method
Big, the not easily shifted and equipment of product is expensive, the problems such as calibration can not be realized in use, causes the accelerometer measures data of unmanned plane
It is inaccurate.
The content of the invention
In view of the problems of the existing technology, the present invention provides a kind of unmanned plane accelerometer school based on ellipsoid fitting
Quasi- method, unmanned plane.
The present invention is achieved in that a kind of unmanned plane accelerometer calibration method based on ellipsoid fitting, this method master
To be applied to the calibration of unmanned plane accelerometer, the unmanned plane accelerometer calibration method based on ellipsoid fitting includes following
Step：
Step 1, Random-Rotation unmanned plane, makes its posture position span cover three dimensions where fitting spheroid as far as possible
Scope, a series of output valve of accelerometer in the case where each test position stationary acquisition obtains different postures.In order to enable calibration
Method is feasible, and the posture of unmanned plane must not be less than six kinds；
Step 2, since accelerometer output valve is integer, so needing to carry out data conversion to output valve, is converted into reality
The acceleration measuring value on border, then according to least square fitting Ellipsoidal Surface, the Ellipsoidal Surface fitted includes ellipsoid
The calibration factor of sphere center position and each axis；
Step 3, calibration is obtained by the sphere center position of the ellipsoid fitted and the calibration factor and calibrating patterns of each axis
Coefficient, including three null offsets and three calibration factors；
Step 4, using the output of six calibration factors and calibrating patterns to each reference axis of unmanned plane accelerometer into
Row compensation, obtains the real measured value of accelerometer.
Further, the calibrating patterns of accelerometer are：
ar=K (am-a0)；
It is unfolded：
Wherein amx、amy、amzFor the measured value of three axis of accelerometer, arx、ary、arzFor the true of three axis of accelerometer
Value, a0x、aoy、a0zFor the zero drift error of three axis of accelerometer, kx、ky、kzFor the calibration factor of three axis of accelerometer.
(calibrating patterns ar=K (am-a0), step 3 has obtained k and a0, the output of accelerometer is am, calculated according to calibrating patterns
As a result)
Further, when the static placement of unmanned plane, three output valve relations of the accelerometer after correction：
Wherein, g represents local gravitational acceleration, then is obtained by calibrating patterns：
Further, the Quadratic Surface Equation of ellipsoid is：
F (ξ, z)=ξTZ=ax2+by2+cz2+ 2dxy+2exz+2fyz+2px+2qy+2rz+t=0；
Wherein ξ=[a, b, c, d, e, f, p, q, r, t]TFor quadratic surface parameter vector to be asked, v=[x2,y2,z2,2xy,
2xz,2yz,2x,2y,2z,1]TFor the computing mix vector of measurement data；F (ξ, v) arrives secondary song for measurement data (x, y, z)
The algebraic distance of face F (ξ, z)；During Quadratic Surface Fitting, the quadratic sum for choosing measurement data to quadratic surface algebraic distance is minimum
For judgment criterion：
Wherein：
The constraints that ellipsoid fitting algorithm based on least square method obtains Ellipsoidal Surface is：
F (ξ, v) matrix of the Quadratic Function Optimization for the best fit Ellipsoidal Surface that least square method with Ellipsoidal Restrictions obtains
Expression can be arranged as vector form：
(X-X0)TA(X-X0)=1；
Wherein,It is the matrix related with three and half axial length of ellipsoid and ellipsoid rotation angle,It is then the center point coordinate of fitting ellipsoid.
Further, obtained according to the measurement calibrating patterns of accelerometer：
(ar)T(ar)=[K (am-a0)]T[K(am-a0)]=| | g | |2；
Arrange：
Contrast ellipsoid fitting formula obtains：
Ellipsoid is fitted, goes out calibration factor using the parametric solution of ellipsoid；Two formula joint solutions can obtain school more than
Quasi- coefficient kx、ky、kzAnd a0x、aoy、a0z。
Another object of the present invention is to provide a kind of unmanned plane accelerometer calibration based on ellipsoid fitting described in
The unmanned plane of method.
Advantages of the present invention and good effect are：Independent of the extraneous large-scale precision equipment as turntable, it is only necessary to
Gathered data under 6 different postures is positioned over by unmanned plane accelerometer is static, calibration algorithm just can rapidly calculate acceleration
Spend meter 3 null offsets and 3 calibration factors, suitable for most occasions such as indoor and outdoor unmanned plane accelerometer it is quick
Calibration.Emulation experiment shows that this method calculation amount is small, and arithmetic speed is fast, can be rapidly completed calibration, it is possible to increase unmanned plane adds
The measurement accuracy of speedometer about 4%, carrys out calibrating accolerometer using turntable and has a substantially suitable precision with existing, but this
Invention substantially operates simpler, and the time used in calibrating accolerometer is obviously shortened, and has larger engineering application value.
Brief description of the drawings
Fig. 1 is the unmanned plane accelerometer calibration method flow diagram provided in an embodiment of the present invention based on ellipsoid fitting.
Fig. 2 is experimental result schematic diagram provided in an embodiment of the present invention；
In figure：(a) X-axis exports；(b) Y-axis exports；(c) Z axis exports.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
The present invention is independent of external device, easy to operate, calibration accuracy is high, can flexibly use in all case, energy
6 coefficients of enough calibrated scale coefficients and null offset etc., improve the measurement accuracy of accelerometer.
The application principle of the present invention is explained in detail below in conjunction with the accompanying drawings.
As shown in Figure 1, the unmanned plane accelerometer calibration method provided in an embodiment of the present invention based on ellipsoid fitting includes
Following steps：
S101：Random-Rotation unmanned plane, makes its posture position span cover three dimensions model where fitting spheroid as far as possible
Enclose, a series of output valve of accelerometer in the case where each test position stationary acquisition obtains different postures；
S102：Ellipsoidal Surface is fitted by the accelerometer output valve measured；
S103：Calibration factor is obtained by the Ellipsoidal Surface fitted；
S104：Compensated using the output of calibration parameter and calibrating patterns to unmanned plane accelerometer.
In a preferred embodiment of the invention：The calibrating patterns of accelerometer are：
ar=K (am-a0)；
Expansion can obtain：
Wherein amx、amy、amzFor the measured value of three axis of accelerometer, arx、ary、arzFor the true of three axis of accelerometer
Value, a0x、aoy、a0zFor the zero drift error of three axis of accelerometer, kx、ky、kzFor the calibration factor of three axis of accelerometer.
The calibration of accelerometer is exactly that the calibration factor of three above zero drift error and three axis is obtained by certain method.
When the static placement of unmanned plane, there is following relation between three output valves of the accelerometer after correction：
Wherein, g represents local gravitational acceleration, then can be obtained by calibrating patterns：
From the foregoing, it will be observed that when if the calibration factor of three axis of accelerometer is not exactly the same, during the measurement of accelerometer just
An ellipsoid can be distributed in.So the present invention is exactly to fit an ellipsoid by measuring multi-group data, then according to plan
The ellipsoid closed out solves the calibration factor of accelerometer, so this calibration method is called ellipsoid fitting.
Ellipsoid is special quadratic surface, and quadric general equation is：
F (ξ, z)=ξTZ=ax2+by2+cz2+ 2dxy+2exz+2fyz+2px+2qy+2rz+t=0；
Wherein ξ=[a, b, c, d, e, f, p, q, r, t]TFor quadratic surface parameter vector to be asked, v=[x2,y2,z2,2xy,
2xz,2yz,2x,2y,2z,1]TFor the computing mix vector of measurement data.F (ξ, v) arrives secondary song for measurement data (x, y, z)
The algebraic distance of face F (ξ, z).During Quadratic Surface Fitting, the quadratic sum for choosing measurement data to quadratic surface algebraic distance is minimum
For judgment criterion, i.e.,：
Wherein：
The basic principle of ellipsoid fitting is exactly to make the quadratic sum of measurement data to the distance of ellipsoidal surfaces minimum, but cannot
The combination of each data is ensured on the curved surface of ellipsoid, therefore it is ellipse to introduce the ellipsoid fitting algorithm acquisition based on least square method
The constraints of ball curved surface is：
F (ξ, v) matrix of the Quadratic Function Optimization for the best fit Ellipsoidal Surface that least square method with Ellipsoidal Restrictions obtains
Expression can be arranged as vector form：
(X-X0)TA(X-X0)=1；
Wherein,It is the matrix related with three and half axial length of ellipsoid and ellipsoid rotation angle,It is then the center point coordinate of fitting ellipsoid.
It can be obtained according to the measurement calibrating patterns of accelerometer：
(ar)T(ar)=[K (am-a0)]T[K(am-a0)]=| | g | |2；
Arrangement can obtain：
Contrast ellipsoid fitting formula can obtain：
As long as from the foregoing, it will be observed that fitting ellipsoid, can just the parametric solution of ellipsoid be utilized to go out calibration factor.
The application effect of the present invention is explained in detail with reference to experiment.
Unmanned plane is calibrated by the accelerometer calibration step of the proposition of the present invention.After the completion of calibration, in order to verify
The validity of the bearing calibration, the static placement straight down of the X-axis of accelerometer accelerates before collection calibration and after calibration respectively
The output of degree three axis of meter is contrasted, and experimental result is as shown in Figure 2
Ideally, the three axis output for calibrating the accelerometer of completion should be respectively 1,0,0.Since there are acceleration
Count and be disposed vertically deviation and noise equal error, three axis of accelerometer are exported under actual conditions has slight error apart from ideal value.
But it was found from being contrasted before calibration with the experimental data after calibration, which significantly reduces the mistake of accelerometer
Difference, improves measurement accuracy.
Unmanned plane accelerometer calibration method based on ellipsoid fitting can quickly and accurately calibrating accolerometer zero
Point drift and calibration factor.Without relying on large-scale precision equipment, only multiple and different postures need to be positioned over by accelerometer is static
.In addition, calculation amount of the present invention is small, arithmetic speed is fast, can be rapidly completed calibration, has certain engineering application value.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
All any modification, equivalent and improvement made within refreshing and principle etc., should all be included in the protection scope of the present invention.
Claims (6)
- A kind of 1. unmanned plane accelerometer calibration method based on ellipsoid fitting, it is characterised in that described based on ellipsoid fitting Unmanned plane accelerometer calibration method comprises the following steps：Step 1, Random-Rotation unmanned plane, makes its posture position span cover three dimensions scope where fitting spheroid as far as possible, A series of output valve of accelerometer in the case where each test position stationary acquisition obtains different postures；Step 2, to output valve data conversion, is converted into actual acceleration measuring value, according to least square fitting ellipsoid Curved surface, the Ellipsoidal Surface fitted include the sphere center position of ellipsoid and the calibration factor of each axis；Step 3, calibration system is obtained by the sphere center position of the ellipsoid fitted and the calibration factor and calibrating patterns of each axis Number, including three null offsets and three calibration factors；Step 4, is mended using the output of six calibration factors and calibrating patterns to each reference axis of unmanned plane accelerometer Repay, obtain the real measured value of accelerometer.
- 2. the unmanned plane accelerometer calibration method based on ellipsoid fitting as claimed in claim 1, it is characterised in that acceleration The calibrating patterns of meter are：ar=K (am-a0)；It is unfolded：<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mi>r</mi> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mi>r</mi> <mi>z</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>k</mi> <mi>x</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>k</mi> <mi>y</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>k</mi> <mi>z</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>*</mo> <mrow> <mo>(</mo> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mi>m</mi> <mi>x</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mi>m</mi> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mi>m</mi> <mi>z</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mn>0</mn> <mi>x</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mn>0</mn> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mn>0</mn> <mi>z</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>)</mo> </mrow> <mo>;</mo> </mrow>Wherein amx、amy、amzFor the measured value of three axis of accelerometer, arx、ary、arzFor the actual value of three axis of accelerometer, a0x、aoy、a0zFor the zero drift error of three axis of accelerometer, kx、ky、kzFor the calibration factor of three axis of accelerometer.
- 3. the unmanned plane accelerometer calibration method based on ellipsoid fitting as claimed in claim 2, it is characterised in that when nobody During the static placement of machine, three output valve relations of the accelerometer after correction：<mrow> <msubsup> <mi>a</mi> <mrow> <mi>r</mi> <mi>x</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>a</mi> <mrow> <mi>r</mi> <mi>y</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>a</mi> <mrow> <mi>r</mi> <mi>z</mi> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <msup> <mi>g</mi> <mn>2</mn> </msup> <mo>;</mo> </mrow>Wherein, g represents local gravitational acceleration, then is obtained by calibrating patterns：<mrow> <msubsup> <mi>k</mi> <mi>x</mi> <mn>2</mn> </msubsup> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>m</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>a</mi> <mrow> <mn>0</mn> <mi>x</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mi>k</mi> <mi>y</mi> <mn>2</mn> </msubsup> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>m</mi> <mi>y</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>a</mi> <mrow> <mn>0</mn> <mi>y</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mi>k</mi> <mi>z</mi> <mn>2</mn> </msubsup> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>m</mi> <mi>z</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>a</mi> <mrow> <mn>0</mn> <mi>z</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <msup> <mi>g</mi> <mn>2</mn> </msup> <mo>.</mo> </mrow>
- 4. the unmanned plane accelerometer calibration method based on ellipsoid fitting as claimed in claim 1, it is characterised in that ellipsoid Quadratic Surface Equation is：F (ξ, z)=ξTZ=ax2+by2+cz2+ 2dxy+2exz+2fyz+2px+2qy+2rz+t=0；Wherein ξ=[a, b, c, d, e, f, p, q, r, t]TFor quadratic surface parameter vector to be asked, v=[x2,y2,z2,2xy,2xz, 2yz,2x,2y,2z,1]TFor the computing mix vector of measurement data；F (ξ, v) arrives quadratic surface F for measurement data (x, y, z) The algebraic distance of (ξ, z)；During Quadratic Surface Fitting, the quadratic sum of selection measurement data to quadratic surface algebraic distance is minimum to be sentenced Disconnected criterion：<mrow> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>&xi;</mi> <mo>&Element;</mo> <msup> <mi>R</mi> <mn>6</mn> </msup> </mrow> </munder> <mo>=</mo> <mo>|</mo> <mo>|</mo> <mi>F</mi> <mrow> <mo>(</mo> <mi>&xi;</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>=</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>&xi;</mi> <mo>&Element;</mo> <msup> <mi>R</mi> <mn>6</mn> </msup> </mrow> </munder> <msup> <mi>&xi;</mi> <mi>T</mi> </msup> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mi>&xi;</mi> <mo>;</mo> </mrow>Wherein：<mrow> <mi>D</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>x</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mtd> <mtd> <msubsup> <mi>y</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mtd> <mtd> <msubsup> <mi>z</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>x</mi> <mn>1</mn> </msub> <msub> <mi>y</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>x</mi> <mn>1</mn> </msub> <msub> <mi>z</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>y</mi> <mn>1</mn> </msub> <msub> <mi>z</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>y</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>z</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mtd> <mtd> <msubsup> <mi>y</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mtd> <mtd> <msubsup> <mi>z</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>x</mi> <mn>2</mn> </msub> <msub> <mi>y</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>x</mi> <mn>2</mn> </msub> <msub> <mi>z</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>y</mi> <mn>2</mn> </msub> <msub> <mi>z</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>y</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>z</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mi>N</mi> <mn>2</mn> </msubsup> </mtd> <mtd> <msubsup> <mi>y</mi> <mi>N</mi> <mn>2</mn> </msubsup> </mtd> <mtd> <msubsup> <mi>z</mi> <mi>N</mi> <mn>2</mn> </msubsup> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>x</mi> <mi>N</mi> </msub> <msub> <mi>y</mi> <mi>N</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>x</mi> <mi>N</mi> </msub> <msub> <mi>z</mi> <mi>N</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>y</mi> <mi>N</mi> </msub> <msub> <mi>z</mi> <mi>N</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>x</mi> <mi>N</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>y</mi> <mi>N</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>z</mi> <mi>N</mi> </msub> </mrow> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>The constraints that ellipsoid fitting algorithm based on least square method obtains Ellipsoidal Surface is：<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfenced open = "|" close = "|"> <mtable> <mtr> <mtd> <mi>a</mi> </mtd> <mtd> <mfrac> <mi>b</mi> <mn>2</mn> </mfrac> </mtd> <mtd> <mfrac> <mi>d</mi> <mn>2</mn> </mfrac> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>b</mi> <mn>2</mn> </mfrac> </mtd> <mtd> <mi>c</mi> </mtd> <mtd> <mfrac> <mi>e</mi> <mn>2</mn> </mfrac> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>d</mi> <mn>2</mn> </mfrac> </mtd> <mtd> <mfrac> <mi>e</mi> <mn>2</mn> </mfrac> </mtd> <mtd> <mi>f</mi> </mtd> </mtr> </mtable> </mfenced> <mo>&NotEqual;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>a</mi> <mi>c</mi> <mo>-</mo> <mfrac> <msup> <mi>b</mi> <mn>2</mn> </msup> <mn>4</mn> </mfrac> <mo>></mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>F (ξ, v) matrix of the Quadratic Function Optimization for the best fit Ellipsoidal Surface that least square method with Ellipsoidal Restrictions obtains represents It can arrange as vector form：(X-X0)TA(X-X0)=1；Wherein,It is the matrix related with three and half axial length of ellipsoid and ellipsoid rotation angle, It is then the center point coordinate of fitting ellipsoid.
- 5. the unmanned plane accelerometer calibration method based on ellipsoid fitting as claimed in claim 4, it is characterised in that according to adding The measurement calibrating patterns of speedometer obtain：(ar)T(ar)=[K (am-a0)]T[K(am-a0)]=| | g | |2；Arrange：<mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>m</mi> </msub> <mo>-</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mfrac> <mrow> <msup> <mrow> <mo>(</mo> <mi>K</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>K</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <mi>g</mi> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>m</mi> </msub> <mo>-</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>;</mo> </mrow>Contrast ellipsoid fitting formula obtains：<mrow> <mi>A</mi> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>(</mo> <mi>K</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>K</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <mi>g</mi> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mfrac> <mo>;</mo> </mrow><mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>X</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>-</mo> <msup> <mi>A</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>p</mi> </mtd> </mtr> <mtr> <mtd> <mi>q</mi> </mtd> </mtr> <mtr> <mtd> <mi>r</mi> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>Ellipsoid is fitted, goes out calibration factor using the parametric solution of ellipsoid.
- 6. a kind of utilize the unmanned plane accelerometer calibration method based on ellipsoid fitting described in 5 any one of Claims 1 to 5 Unmanned plane.
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