CN104459828A - Geomagnetism vector system non-alignment correction method based on axis rotating method - Google Patents

Abstract

The invention belongs to the technical field of magnetic measurement and particularly provides a geomagnetism vector system non-alignment correction method based on an axis rotating method. The method comprises the following steps that 1, a non-magnetic rotating table is arranged; 2, a magnetic sensor and an acceleration meter in a geomagnetism vector system are packaged into a non-magnetic regular hexahedron; 3, the non-magnetic regular hexahedron is arranged on a table board of the non-magnetic rotating table to ensure that the X-axis direction of the non-magnetic regular hexahedron is identical with the direction of a rotating shaft, and the rotating shaft rotates around the X-axis for N1 times to obtain N1 sets of measurement values of the magnetic sensor and the acceleration meter; 4, the Z-axis direction of the non-magnetic regular hexahedron is kept to be identical with the direction of the rotating shaft, and the rotating shaft rotates around the Z-axis for N2 times to obtain N2 sets of measurement values of the magnetic sensor and the acceleration meter; 5, the non-alignment angle from the magnetic sensor to the non-magnetic regular hexahedron and the non-alignment angle from the acceleration meter to the non-magnetic regular hexahedron are calculated respectively; 6, correction is finished by determining the coordinate converting relation between the magnetic sensor and the acceleration meter.

Description

Based on the non-aligned bearing calibration of earth magnetism vector system around method of principal axes

Technical field

The invention belongs to Magnetic Measurement Technology field, be specifically related to a kind of non-aligned error calibration method for earth magnetism vector measurement system.

Background technology

Magnetic sensor is widely used owing to providing component information, and its measured value is the size that terrestrial magnetic field projects in Magnetic Sensor three sensitive axes.If the Eulerian angle relation between the rectangular coordinate system that known Magnetic Sensor three sensitive axes are formed and geographic coordinate system, then can calculate the ground magnetic component under geographic coordinate system: north component of geomagnetic field, east component, vertical component.How effectively to obtain under geographic coordinate system magnetic component be exactly earth magnetism vector measurement problem, earth magnetism vector measurement has then been come by earth magnetism vector measurement system.Earth magnetism vector measurement need use magnetic sensor, needs to determine Magnetic Sensor orientation simultaneously, solves magnetic sensor and determines appearance problem.Accuracy of attitude determination is the key factor of vector measurement, and vector measurement be made to reach certain precision, is very strict for the requirement determining appearance.

Earth magnetism vector measurement system is formed primarily of Magnetic Sensor and the direct strapdown of inertial navigation, and Magnetic Sensor is used for measuring the magnetic-field component of Magnetic Sensor coordinate system, and inertial navigation is then for Magnetic Sensor provides various attitude information: the angle of course, pitching, roll.By three components of the magnetic vector that can obtain in geographic coordinate system that converts, wherein inertial navigation comprises three axle gyro and three axis accelerometers, and in earth magnetism vector system, accelerometer coordinate system and gyro coordinate system can think consistent.Inevitably there are some errors in earth magnetism vector measurement system, wherein, Magnetic Sensor measures axle and the inertial navigation coordinate system error measured between axle is called " non-aligned error " in installation process." non-aligned error " becomes the key factor affecting magnetic element measuring accuracy, is difficult to solve non-aligned problem by mechanical registeration method.Under ground magnetic environment, the non-aligned error of 1 ° can cause the vector measurement error of hundreds of nT (nT is unit of magnetic field strength).Therefore non-aligned error correction techniques is studied significant to raising earth magnetism vector measurement system precision.Due to inertial navigation coordinate system and Magnetic Sensor coordinate system all not visible, and correct different from sensor coordinate system in array, inertial navigation and Magnetic Sensor measure different physical quantitys, increase correction difficulty.

For the non-aligned error of different system, some scholars propose relevant bearing calibration.People (the Rong Zhu such as Rong Zhu, Zhaoying Zhou, Calibration of three-dimensional integrated sensors forimproved system accuracy, Sensors and Actuators A 127 (2006) 340 – 344) adopt regular hexahedron optical prism and orthogonal optical coordinate system system, to MEMS (micro electro mechanical system) (MEMS, Micro-Electro-MechanicalSystem) the non-aligned error of integrated transducer system corrects, utilize magnetic field and the gravity projection value of optical system coordinate system, calculate Magnetic Sensor and the accelerometer non-aligned error to optical system coordinate system respectively.But the method needs accurate adjustment optical system three-dimensional system of coordinate, need by when earth's magnetic dip angle information, and ensure regular hexahedron optical prism initial coordinate system and north, locality, east, coordinate system consistent.Therefore the method to optical system and optical prism initial coordinate system adjustment exact requirements high.People (the Erin L.Renk such as Erin L.Renk, W.C., Matthew Rizzo, Fuju Lee, andDennis S.Bernstein.Calibrating a Triaxial Accelerometer-Magnetometer.IEEE ControlSystems Magazine (2005) 86 – 95) adopt sextuple degree of freedom robot to correct non-aligned error; Equally, the method needs accurately to control attitude, needs to provide course angle, the angle of pitch, roll angle, complicated operation.The people such as J.Vcelak (J.Vcelak, P.Ripka, J.Kubik, A.Platil and P.Kaspar, AMR navigation systems and methods oftheir calibration, Sensors and Actuators A 123 – 124 (2005) 122 – 128) utilize without the non-aligned error of magnetic turntable correcting electronic magnetic compass, estimate non-aligned angle by the method for platform wherein two axles that rotate.Its core concept be to utilize the magnetic field of rotating shaft direction and gravity constant, thus calculate the non-aligned error of Magnetic Sensor and accelerometer respectively.The method needs the attitude information provided by accelerometer when the non-aligned error of calculating Magnetic Sensor roll angle.In addition, said method have ignored the non-aligned error of roll angle of accelerometer when Modling model.David Jurman (DavidJurman, Marko Jankovec, Roman Kamnik, Marko Topic, Calibration and data fusion solutionfor the miniature attitude and heading reference system, Sensors and Actuators A 138 (2007) 411 – 420) etc. people for MEMS magnetic compass, Magnetic Sensor and accelerometer package in the plastic resin material regular hexahedron of an opening, its bearing calibration principle is the same with people's methods such as J.Vcelak, difference is have employed without magnetic recording level plate, need equally to provide attitude information.

About the non-aligned correction of earth magnetism vector measurement system, the people such as Pang Hongfeng have applied for national inventing patent (application number: 201210355541.7, for the non-aligned error calibration method of magnetic element measuring system, the day for announcing: on January 16th, 2013) adopt perpendicular type table top and positive six casings, by repeatedly overturning without magnetic regular hexahedron, order upset after without magnetic regular hexahedron still near perpendicular type table top.Utilize gravitational vector at perpendicular type table top projection components invariance principle, the non-aligned angle between calculating magnetic field sensor and inertial navigation system.Flatness and the verticality of the method requirement perpendicular type table top are very high, and each upset all requires that table top and casing closely agree with.The method all requires higher to the machining precision of equipment and performance accuracy.In addition, because the earth magnetism projection components value of perpendicular type table top and non-aligned angle are solve for parameter, therefore solve for parameter is many, and earth magnetism projection components value and non-aligned angular dimensions intercouple, degree is high.

Generally speaking, all there is the deficiency such as equipment and complicated operation in the bearing calibration of the non-aligned angle error of above-mentioned earth magnetism vector system, requires higher, or need accurately to provide attitude information, have impact on correction accuracy to experimental facilities and researcher's operating experience.

Summary of the invention

For the technical matters that prior art exists, the invention provides the non-aligned error calibration method for earth magnetism vector measurement system that a kind of original paper simply, easily realizes, easy to operate, correction accuracy is higher.

Concrete technical scheme is as follows:

Based on the non-aligned bearing calibration of earth magnetism vector system around method of principal axes, comprise the following steps:

(S1) arrange without magnetic turntable, comprise a pedestal, a table top and a turning axle, described rotation axis vertically connects pedestal and table top;

(S2) by the Magnetic Sensor in earth magnetism vector measurement system and accelerometer package in without in magnetic regular hexahedron, if be XYZ without the coordinate of magnetic regular hexahedron;

(S3) be positioned on the table top without magnetic turntable by without magnetic regular hexahedron, keep consistent with turning axle direction without the X-direction of magnetic regular hexahedron, rotate and make to rotate unspecified angle without magnetic regular hexahedron around X-axis without magnetic turntable table top, the measured value of record Magnetic Sensor and accelerometer, rotates N around X-axis altogether ₁secondary, obtain N ₁the measured value of group Magnetic Sensor and accelerometer;

(S4) upset is without magnetic regular hexahedron, keep consistent with turning axle direction without the Z-direction of magnetic regular hexahedron, rotate and make to rotate unspecified angle without magnetic regular hexahedron around Z axis without magnetic turntable table top, the measured value of record Magnetic Sensor and accelerometer, rotates N around Z axis altogether ₂secondary, obtain N ₂the measured value of group Magnetic Sensor and accelerometer;

(S5) according to the N obtaining Magnetic Sensor and accelerometer ₁group and N ₂group measured value, according to the magnetic field on turning axle direction and weight component invariance principle, calculate respectively Magnetic Sensor to without the non-aligned angle of magnetic regular hexahedron and accelerometer to the non-aligned angle without magnetic regular hexahedron;

(S6) according to Magnetic Sensor to without the non-aligned angle of magnetic regular hexahedron and accelerometer to the non-aligned angle without magnetic regular hexahedron, determine the ordinate transform relation between Magnetic Sensor and accelerometer, namely complete correction.

Further, in described step (S5) according to the N of Magnetic Sensor and accelerometer ₁group and N ₂group measured value, calculating Magnetic Sensor to the non-aligned angle detailed process without magnetic regular hexahedron is:

(S501) according to following formula, Magnetic Sensor measured value, field projection value and non-aligned angular dependence is set up:

$H^x=H_{\mathrm{mag}}^{\mathrm{xx}}{a}_{11}+H_{\mathrm{mag}}^{\mathrm{xy}}{a}_{21}+H_{\mathrm{mag}}^{\mathrm{xz}}{a}_{31},$

$H^z=H_{\mathrm{mag}}^{\mathrm{zx}}{a}_{13}+H_{\mathrm{mag}}^{\mathrm{zy}}{a}_{23}+H_{\mathrm{mag}}^{\mathrm{zz}}{a}_{33},$

Wherein, for without magnetic regular hexahedron Magnetic Sensor measured value when X-axis rotates, for without magnetic regular hexahedron Magnetic Sensor measured value when Z axis rotates; H ^xfor without magnetic regular hexahedron when X-axis rotates, terrestrial magnetic field is without magnetic regular hexahedron X-axis projection value; H ^zfor without magnetic regular hexahedron when Z axis rotates, terrestrial magnetic field is without magnetic regular hexahedron Z axis projection value; $\left\{\begin{array}{c}{a}_{11}=\cos {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\β}}_{\mathrm{mag}}\\ a_{21}=-\sin {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\β}}_{\mathrm{mag}}\\ a_{31}=\cos {\mathrm{\β}}_{\mathrm{mag}}\end{array}\right.,$ $\left\{\begin{array}{c}{a}_{13}=\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}-\cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ a_{23}=\cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}+\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ a_{33}=\cos {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\end{array}\right.,$ α _mag, β _mag, γ _magrepresent Magnetic Sensor and without the non-aligned angle between magnetic regular hexahedron;

(S502) according to following formula, N is utilized ₁group and N ₂group measured value calculates Magnetic Sensor and without the non-aligned angle α between magnetic regular hexahedron _mag, β _mag, γ _mag:

$\left\{\begin{array}{c}{H}^x=H_{\mathrm{mag}}^{\mathrm{xx}1}{a}_{11}+H_{\mathrm{mag}}^{\mathrm{xy}1}{a}_{21}+H_{\mathrm{mag}}^{\mathrm{xz}1}{a}_{31}\\ H^x=H_{\mathrm{mag}}^{\mathrm{xx}2}{a}_{11}+H_{\mathrm{mag}}^{\mathrm{xy}2}{a}_{21}+H_{\mathrm{mag}}^{\mathrm{xz}2}{a}_{31}\\ \·\\ \·\\ \·\\ H^x=H_{\mathrm{mag}}^{\mathrm{xx}{N}_1}{a}_{11}+H_{\mathrm{mag}}^{\mathrm{xx}{N}_1}{a}_{21}+H_{\mathrm{mag}}^{\mathrm{xz}{N}_1}{a}_{31}\end{array}\right.$ With $\left\{\begin{array}{c}{H}^z=H_{\mathrm{mag}}^{\mathrm{zx}1}{a}_{13}+H_{\mathrm{mag}}^{\mathrm{zy}1}{a}_{23}+H_{\mathrm{mag}}^{\mathrm{zz}1}{a}_{33}\\ H^z=H_{\mathrm{mag}}^{\mathrm{zx}2}{a}_{13}+H_{\mathrm{mag}}^{\mathrm{zy}2}{a}_{23}+H_{\mathrm{mag}}^{\mathrm{zz}2}{a}_{33}\\ \·\\ \·\\ \·\\ H^z=H_{\mathrm{mag}}^{\mathrm{zx}{N}_2}{a}_{13}+H_{\mathrm{mag}}^{\mathrm{zy}{N}_2}{a}_{23}+H_{\mathrm{mag}}^{\mathrm{zz}{N}_2}{a}_{33}\end{array}\right.;$

Wherein, indicate without the magnetic regular hexahedron N that Magnetic Sensor exports when X-axis rotates ₁group measured value; indicate without the magnetic regular hexahedron N that Magnetic Sensor exports when Z axis rotates ₂group measured value;

In described step (S5), calculating accelerometer to the detailed process at the non-aligned angle without magnetic regular hexahedron is:

(S511) according to following formula, acceleration measuring value, gravity projection value and non-aligned angular dependence is set up,

$g^x=g_m^{\mathrm{xx}}{b}_{11}+g_m^{\mathrm{xy}}{b}_{21}+g_m^{\mathrm{xz}}{b}_{31},$

$g^z=g_m^{\mathrm{zx}}{b}_{11}+g_m^{\mathrm{zy}}{b}_{23}+g_m^{\mathrm{zz}}{b}_{33},$

Wherein, for rotating brief acceleration measurement value without magnetic regular hexahedron around X-axis, for without magnetic regular hexahedron Magnetic Sensor measured value when Z axis rotates, g ^xfor without magnetic regular hexahedron when X-axis rotates, gravity is without magnetic regular hexahedron X-axis projection value; g ^zfor without magnetic regular hexahedron when Z axis rotates, gravity is without magnetic regular hexahedron Z axis projection value; $\left\{\begin{array}{c}{b}_{11}=\cos {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\β}}_{\mathrm{acc}}\\ b_{21}=-\sin {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\β}}_{\mathrm{acc}}\\ b_{31}=\sin {\mathrm{\β}}_{\mathrm{acc}}\end{array}\right.,$ $\left\{\begin{array}{c}{b}_{13}=\sin {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}-\cos {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\\ b_{23}=\cos {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}+\sin {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\\ b_{33}=\cos {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\end{array}\right.,$ α _acc, β _acc, γ _accfor accelerometer and without the non-aligned angle between magnetic regular hexahedron;

(S512) according to following formula, N is utilized ₁group and N ₂group measured value calculates accelerometer and without the non-aligned angle α between magnetic regular hexahedron _acc, β _acc, γ _acc:

$\left\{\begin{array}{c}{g}^x=g_m^{\mathrm{xx}1}{b}_{11}+g_m^{\mathrm{xy}1}{b}_{21}+g_m^{\mathrm{xz}1}{b}_{31}\\ g^x=g_m^{\mathrm{xx}2}{b}_{11}+g_m^{\mathrm{xy}2}{b}_{21}+g_m^{\mathrm{xz}2}{b}_{31}\\ \·\\ \·\\ \·\\ g^x=g_m^{\mathrm{xxN}1}{b}_{11}+g_m^{\mathrm{xxN}1}{b}_{21}+g_m^{\mathrm{xzN}1}{b}_{31}\end{array}\right.$ With $\left\{\begin{array}{c}{g}^z=g_m^{\mathrm{zx}1}{a}_{13}+g_m^{\mathrm{zy}1}{a}_{23}+g_m^{\mathrm{zz}1}{a}_{33}\\ g^z=g_m^{\mathrm{zx}2}{a}_{13}+g_m^{\mathrm{zy}2}{a}_{23}+g_m^{\mathrm{zz}2}{a}_{33}\\ \·\\ \·\\ \·\\ g^z=g_m^{\mathrm{zxN}2}{a}_{13}+g_m^{\mathrm{zyN}2}{a}_{23}+g_m^{\mathrm{zzN}2}{a}_{33}\end{array}\right.$

Wherein, indicate the N rotating the output of brief acceleration meter without magnetic regular hexahedron around X-axis ₁group measured value; indicate the N rotating the output of brief acceleration meter without magnetic regular hexahedron around Z axis ₂group measured value.

Further, the detailed process of described step (S6) is:

(S61) according to α _mag, β _mag, γ _mag, realize Magnetic Sensor measured value be converted to magnetic field at the projection value without magnetic regular hexahedron computing formula is as follows:

$\left[\begin{array}{c}{B}_L^x\\ B_L^y\\ B_L^z\end{array}\right]=\left[\begin{array}{ccc}\cos {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\β}}_{\mathrm{mag}}& \sin {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}+\cos {\mathrm{\α}}_{\mathrm{mag}}{\sin \mathrm{\β}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}& \sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}-\cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ -\sin {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\β}}_{\mathrm{mag}}& \cos {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}-\sin {\mathrm{\α}}_{\mathrm{mag}}{\sin \mathrm{\β}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}& \cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}+\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ \sin {\mathrm{\β}}_{\mathrm{mag}}& -\cos {\mathrm{\β}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}& \cos {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\end{array}\right]\·\left[\begin{array}{c}{H}_{\mathrm{mag}}^x\\ H_{\mathrm{mag}}^y\\ H_{\mathrm{mag}}^z\end{array}\right];$

(S62) according to α _acc, β _acc, γ _acc, realize be transformed into the field projection value of accelerometer coordinate system computing formula is as follows:

$\left[\begin{array}{c}{B}_{\mathrm{mag}}^x\\ B_{\mathrm{mag}}^y\\ B_{\mathrm{mag}}^z\end{array}\right]={\left[\begin{array}{ccc}\cos {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\β}}_{\mathrm{acc}}& \sin {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}+\cos {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}& \sin {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}-\cos {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\\ -\sin {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\β}}_{\mathrm{acc}}& \cos {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}-\sin {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}& \cos {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}+\sin {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\\ \sin {\mathrm{\β}}_{\mathrm{acc}}& -\cos {\mathrm{\β}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}& \cos {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\end{array}\right]}^{-1}\·\left[\begin{array}{c}{H}_L^x\\ H_L^y\\ H_L^z\end{array}\right];$

Therefore, obtain the ordinate transform relation between Magnetic Sensor and accelerometer, namely complete correction.

Further, described Magnetic Sensor adopts magnetic sensor, and described accelerometer adopts three axis accelerometer.

Further, described is the regular hexahedron adopting plastic resin material to make without magnetic regular hexahedron.

In order to the non-aligned angle of satisfied calculating is representative, fully encourage error parameter, the Magnetic Sensor measurement data rotated around disalignment all uses. for Magnetic Sensor measures output valve, after non-aligned error correction, magnetic field is at the projection value of accelerometer coordinate system.After non-aligned error correction, the coordinate system of Magnetic Sensor is consistent with accelerometer, then directly can carry out earth magnetism vector measurement.

Compared with prior art, the technique effect of acquisition of the present invention is adopted to be: 1, after bearing calibration application of the present invention, whole calibration equipment is simple, without the need to the perpendicular type table top of machining high-precision, only needs one and can calculate non-aligned angle without magnetic rotation structure and regular hexahedron easily.2, after bearing calibration of the present invention application, significantly reduce without magnetic regular hexahedron processing request, without the need to requiring all there is high verticality without between each face of magnetic regular hexahedron, only needing to ask between two faces there is higher verticality.3, bearing calibration of the present invention, whole trimming process is simple to operate, without the need to carrying out full attitude upset to without magnetic regular hexahedron, also closely agreeing with without magnetic regular hexahedron and perpendicular type table top without the need to being strict with, only needing under stabilizing magnetic field environment, swaying without magnetic regular hexahedron, the initial attitude that system is placed is not strict with, do not need accurately to control rotational angle, sense of rotation is not also strict with, and reduces experiment difficulty.4, bearing calibration of the present invention, parameter estimation model is simplified, and solve for parameter is only containing non-aligned angle, and parameter couples degree reduces, and reduces parameter estimation algorithm requirement.5, bearing calibration of the present invention, to the non-aligned correction of Magnetic Sensor without the need to introducing attitude information, earth's magnetic dip angle, the supplementary such as geographic orientation and optical system of accelerometer.

Accompanying drawing explanation

Fig. 1 is schematic flow sheet of the present invention;

Fig. 2 is the schematic diagram of the present invention when being in original state in embody rule example;

Fig. 3 rotates schematic diagram without magnetic regular hexahedron around X-axis;

Fig. 4 rotates schematic diagram without magnetic regular hexahedron around Z axis;

Fig. 5 is that Magnetic Sensor and accelerometer are to the non-aligned angle schematic diagram without magnetic regular hexahedron.

Marginal data:

1, pedestal; 2, rotation axis; 3, table top; 4, without magnetic regular hexahedron; 5, Magnetic Sensor; 6, accelerometer; 7, magnetic vector projects along rotation axis; 8, gravitational vector projects along rotation axis; 9, without magnetic regular hexahedron coordinate system XYZ.

Embodiment

In order to better understand technical scheme of the present invention, now its principle and formula proving are described in detail as follows:

The non-aligned error calibration method that the present invention is used for earth magnetism vector measurement system is: Magnetic Sensor 5 and accelerometer 6 are encapsulated into one without in magnetic regular hexahedron 4, is transformed and the relation without magnetic regular hexahedron coordinate system 9 by the coordinate system relation indirect of two kinds of sensors; To be positioned over without magnetic turntable table top 3 without magnetic regular hexahedron 4.Rotate without magnetic regular hexahedron 4, in rotation process, magnetic vector rotation axis projection 7 can use Magnetic Sensor 5 measured value and non-aligned angle analytic representation.Non-aligned error angle is unknown parameter, utilizes the measured value of Magnetic Sensor 5 in rotation process to set up Nonlinear System of Equations, thus the coordinate calculating Magnetic Sensor 5 is tied to the non-aligned error without magnetic regular hexahedron 4.In like manner, accelerometer 6 can be calculated to the non-aligned error without magnetic regular hexahedron 4, thus realize the non-aligned error correction between Magnetic Sensor 5 and accelerometer 6.

As shown in Figure 1, the concrete implementation step of the inventive method is:

1. be positioned over steady ground without magnetic rotary table base 1, place without the need to severity.

2. see Fig. 2, by the Magnetic Sensor 5 of earth magnetism vector measurement system and accelerometer 6 integral packaging in one without in magnetic regular hexahedron 4, Magnetic Sensor 5 and accelerometer 6 strapdown; This is positioned over without magnetic turntable table top 1 without magnetic regular hexahedron 4.Set up without magnetic regular hexahedron 4 without magnetic regular hexahedron coordinate system 9, be X, Y, Z without magnetic regular hexahedron coordinate system 9 coordinate axis; As shown in Figure 5, Magnetic Sensor and accelerometer are to the non-aligned angle schematic diagram without magnetic regular hexahedron.

In this example, as shown in Figure 2, when initial position, X-axis without the coordinate system 9 of magnetic regular hexahedron 4 is parallel with rotation axis, magnetic vector projects 8 along rotation axis projection 7 and gravitational vector along rotation axis, is magnetic vector and projects without magnetic regular hexahedron X-axis along without the projection of magnetic regular hexahedron X-axis and gravitational vector edge.Magnetic Sensor 5 adopts magnetic sensor, and accelerometer 6 adopts three axis accelerometer.Terrestrial magnetic field is being designated as without the projection of magnetic regular hexahedron coordinate system 9 magnetic Sensor measured value is both sides relation is as follows:

$\left[\begin{array}{c}{H}^x\\ H_{L0}^y\\ H_{L0}^z\end{array}\right]\left[\begin{array}{ccc}{s}_{11}& a_{12}& a_{13}\\ s_{21}& a_{22}& a_{23}\\ s_{31}& a_{32}& a_{33}\end{array}\right]\left[\begin{array}{c}{H}_{\mathrm{mag}}^x\\ H_{\mathrm{mag}}^y\\ H_{\mathrm{mag}}^z\end{array}\right]---\left(1\right)$

Formula (1) is converted into:

$\left\{\begin{array}{c}{H}^x=H_{\mathrm{mag}}^x{a}_{11}+H_{\mathrm{mag}}^y{a}_{21}+H_{\mathrm{mag}}^z{a}_{31}\\ H_{L0}^y=H_{\mathrm{mag}}^x{a}_{12}+H_{\mathrm{mag}}^y{a}_{22}+H_{\mathrm{mag}}^z{a}_{32}\\ H_{L0}^z=H_{\mathrm{mag}}^x{a}_{13}+H_{\mathrm{mag}}^y{a}_{23}+H_{\mathrm{mag}}^z{a}_{33}\end{array}\right.---\left(2\right)$

Wherein

$\left\{\begin{array}{c}{a}_{11}=\cos {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\β}}_{\mathrm{mag}}\\ a_{12}=\sin {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}+\cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}\\ a_{13}=\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}-\cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ a_{21}=-\sin {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\β}}_{\mathrm{mag}}\\ a_{22}=\cos {\mathrm{\α}}_{\mathrm{mad}}\cos {\mathrm{\γ}}_{\mathrm{mag}}-\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}\\ a_{23}=\cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}+\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ a_{31}=\sin {\mathrm{\β}}_{\mathrm{mag}}\\ a_{32}=-\cos {\mathrm{\β}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}\\ a_{33}=\cos {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{maag}}\end{array}\right.---\left(3\right)$

Wherein, α _mag, β _mag, γ _magit is Magnetic Sensor 5 and without the non-aligned angle between magnetic regular hexahedron coordinate system 9.

3. as shown in Figure 3, rotate without magnetic turntable table top 3, then rotate around its X-axis without magnetic regular hexahedron 4, terrestrial magnetic field is at the X-axis projection H without magnetic regular hexahedron coordinate system 9 ^xconstant.Record Magnetic Sensor 5 measured value to be designated as simultaneously in rotation process, Magnetic Sensor 5 measured value and the H that projects without the X-axis terrestrial magnetic field of magnetic regular hexahedron coordinate system 9 ^xrelation is as follows:

$H^x=H_{\mathrm{mag}}^{\mathrm{xx}}{a}_{11}+H_{\mathrm{mag}}^{\mathrm{xy}}{a}_{21}+H_{\mathrm{mag}}^{\mathrm{xz}}{a}_{31}---\left(4\right)$

If non-aligned angular error is zero, then a ₁₁=1, a ₂₁=0, a ₃₁=0, then in rotation process, measure N ₁group Magnetic Sensor output valve.Adopt nonlinear least square method solution Nonlinear System of Equations, carry out parameter estimation, calculate α _mag, β _mag.Such as formula (5):

$\left\{\begin{array}{c}{H}^x=H_{\mathrm{mag}}^{\mathrm{xx}1}{a}_{11}+H_{\mathrm{mag}}^{\mathrm{xy}1}{a}_{21}+H_{\mathrm{mag}}^{\mathrm{xz}1}{a}_{31}\\ H^x=H_{\mathrm{mag}}^{\mathrm{xx}2}{a}_{11}+H_{\mathrm{mag}}^{\mathrm{xy}2}{a}_{21}+H_{\mathrm{mag}}^{\mathrm{xz}2}{a}_{31}\\ \·\\ \·\\ \·\\ H^x=H_{\mathrm{mag}}^{\mathrm{xx}{N}_1}{a}_{11}+H_{\mathrm{mag}}^{\mathrm{xx}{N}_1}{a}_{21}+H_{\mathrm{mag}}^{\mathrm{xz}{N}_1}{a}_{31}\end{array}\right.---\left(5\right)$

Wherein:

$\left\{\begin{array}{c}{a}_{11}=\cos {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\β}}_{\mathrm{mag}}\\ a_{21}=-\sin {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\β}}_{\mathrm{mag}}\\ a_{31}=\sin {\mathrm{\β}}_{\mathrm{mag}}\end{array}\right.---\left(6\right)$

4. known, rotate around the X-axis without magnetic regular hexahedron coordinate system 9, only can calculate α _mag, β _mag, cannot γ be calculated _mag.As shown in Figure 4, the Z axis without magnetic regular hexahedron coordinate system 9 rotates.In rotation process, Magnetic Sensor 5 measured value and the terrestrial magnetic field H without the Z axis of magnetic regular hexahedron coordinate system 9 ^zrelation is as follows:

$H^z=H_{\mathrm{mag}}^{\mathrm{zx}}{a}_{13}+H_{\mathrm{mag}}^{\mathrm{zy}}{a}_{23}+H_{\mathrm{mag}}^{\mathrm{zz}}{a}_{33}---\left(7\right)$

In rotation process, obtain the N that Magnetic Sensor exports ₂group measured value.Adopt nonlinear least square method solution Nonlinear System of Equations, carry out parameter estimation, calculate γ _mag, as shown in the formula:

$\left\{\begin{array}{c}{H}^z=H_{\mathrm{mag}}^{\mathrm{zx}1}{a}_{13}+H_{\mathrm{mag}}^{\mathrm{zy}1}{a}_{23}+H_{\mathrm{mag}}^{\mathrm{zz}1}{a}_{33}\\ H^z=H_{\mathrm{mag}}^{\mathrm{zx}2}{a}_{13}+H_{\mathrm{mag}}^{\mathrm{zy}2}{a}_{23}+H_{\mathrm{mag}}^{\mathrm{zz}2}{a}_{33}\\ \·\\ \·\\ \·\\ H^z=H_{\mathrm{mag}}^{\mathrm{zx}{N}_2}{a}_{13}+H_{\mathrm{mag}}^{\mathrm{zy}{N}_2}{a}_{23}+H_{\mathrm{mag}}^{\mathrm{zz}{N}_2}{a}_{33}\end{array}\right.---\left(8\right)$

Wherein:

$\left\{\begin{array}{c}{a}_{13}=\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}-\cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ a_{23}=\cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}+\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ a_{33}=\cos {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\end{array}\right.---\left(9\right)$

In order to the better estimated parameter of energy, preferably use the data of different attitude, the data namely rotating and rotate around Z output without magnetic regular hexahedron around X adopt simultaneously and calculate.

Calculate α _mag, β _mag, γ _magafter, take back formula (1) counter for non-aligned parameter, the Magnetic Sensor measured value rotated can be corrected to hexahedron coordinate system field projection value around X-axis, the error according to correcting between front and back X-axis measured value and actual value contrasts, to the α estimated _mag, β _mag, γ _magassess.

5. in like manner, without magnetic regular hexahedron when X-axis rotates, accelerometer 6 measured value projecting without magnetic regular hexahedron coordinate system 9 with gravity pass is:

$\left[\begin{array}{c}{g}^x\\ g_{L0}^y\\ g_{L0}^z\end{array}\right]\left[\begin{array}{ccc}{b}_{11}& b_{12}& b_{13}\\ b_{21}& b_{22}& b_{23}\\ b_{31}& b_{32}& b_{33}\end{array}\right]\left[\begin{array}{c}{g}_m^x\\ g_m^y\\ g_m^z\end{array}\right]---\left(10\right)$

Obtain accelerometer 6 and the non-aligned angle without magnetic regular hexahedron coordinate system 9, operate computation process and Magnetic Sensor just the same.In the X-axis rotation process without magnetic regular hexahedron coordinate system 9, angle error is there is due to accelerometer 6 coordinate system and without between magnetic regular hexahedron coordinate system 9, therefore angle constantly changes between gravitational vector rotation axis projection 8 and the X-axis of accelerometer 6, the X-axis of accelerometer 6 is caused to export constantly fluctuation.When rotating respectively without the X-axis of magnetic regular hexahedron coordinate system 9 and Z axis, the output valve of record accelerometer 6 simultaneously.

Nonlinear least square method is adopted to carry out parameter estimation, by solving equations calculating accelerometer and without the non-aligned angle α between magnetic regular hexahedron _acc, β _acc, γ _acc.

Calculate α _acc, β _acc, γ _accafter, take back formula (10) counter for non-aligned angular dimensions, the acceleration measuring value rotated can be corrected to hexahedron coordinate system gravity projection value around X-axis, the error according to correcting between front and back X-axis measured value and actual value contrasts, to the α estimated _acc, β _acc, γ _accassess.

6. α is calculated _mag, β _mag, γ _magand α _acc, β _acc, γ _accafter, can non-aligned angle indirectly between corrected acceleration meter 6 and Magnetic Sensor 5.Magnetic Sensor 5 measured value is carried out to the correction of non-aligned error, the conversion namely between Magnetic Sensor coordinate system and accelerometer coordinate system.First, according to α _mag, β _mag, γ _mag, realize Magnetic Sensor measured value be converted to magnetic field at the projection value B without magnetic regular hexahedron _l ^x, B _l ^y, B _l ^z, computation process as shown in the formula:

$\begin{array}{c}\left[\begin{array}{c}{B}_L^x\\ B_L^y\\ B_L^z\end{array}\right]=\left[\begin{array}{ccc}\cos {\mathrm{\α}}_{\mathrm{mag}}{\cos \mathrm{\β}}_{\mathrm{mag}}& \sin {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}+\cos {\mathrm{\α}}_{\mathrm{mag}}{\sin \mathrm{\β}}_{\mathrm{mag}}{\sin \mathrm{\γ}}_{\mathrm{mag}}& \sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}-\cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ -\sin {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\β}}_{\mathrm{mag}}& \cos {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}-\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}& \cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}+\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ \sin {\mathrm{\β}}_{\mathrm{mag}}& -\cos {\mathrm{\β}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}& \cos {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\end{array}\right]\\ \·\left[\begin{array}{c}{H}_{\mathrm{mag}}^x\\ H_{\mathrm{mag}}^y\\ H_{\mathrm{mag}}^z\end{array}\right]\end{array}---\left(11\right)$

Secondly, according to α _acc, β _acc, γ _acc, realize be transformed into the field projection value of accelerometer coordinate system as shown in the formula:

$\begin{array}{c}\left[\begin{array}{c}{B}_{\mathrm{mag}}^x\\ B_{\mathrm{mag}}^y\\ B_{\mathrm{mag}}^z\end{array}\right]={\left[\begin{array}{ccc}\cos {\mathrm{\α}}_{\mathrm{acc}}{\cos \mathrm{\β}}_{\mathrm{acc}}& \sin {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{a\; cc}}+\cos {\mathrm{\α}}_{\mathrm{acc}}{\sin \mathrm{\β}}_{\mathrm{acc}}{\sin \mathrm{\γ}}_{\mathrm{acc}}& \sin {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}-\cos {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\\ -\sin {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\β}}_{\mathrm{acc}}& \cos {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}-\sin {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}& \cos {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}+\sin {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\\ \sin {\mathrm{\β}}_{\mathrm{acc}}& -\cos {\mathrm{\β}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}& \cos {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\end{array}\right]}^{-1}\\ \·\left[\begin{array}{c}{H}_L^x\\ H_L^y\\ H_L^z\end{array}\right]\end{array}---\left(12\right)$

Wherein, for Magnetic Sensor measured value, (namely Magnetic Sensor is relative to the component of himself coordinate system, in trimming process, ordinate transform is divided into two steps, first be that Magnetic Sensor measured value is transformed into without magnetic regular hexahedron coordinate system projection value, next is transformed into accelerometer coordinate system projection value without magnetic regular hexahedron coordinate system projection value) after non-aligned error correction, magnetic field is at the projection value of accelerometer coordinate system.After non-aligned error correction, the coordinate system of Magnetic Sensor is consistent with accelerometer, then directly can carry out earth magnetism vector measurement.

Below, in conjunction with specific embodiments the present invention is described in further details.

By triaxial magnetic field sensor and inertial navigation system (containing accelerometer), be fixedly installed in without in magnetic regular hexahedron.In countryside, Changsha, Hunan, select a physical features flat country, carry out non-aligned correction.Preset Magnetic Sensor and without the non-aligned angle between magnetic regular hexahedron: [α _magβ _magγ _mag]=[0.5 ° 0.8 ° 0.9 °]; Preset accelerometer and without the non-aligned angle between magnetic regular hexahedron: [α _accβ _accγ _acc]=[0.6 ° 0.8 ° 1 °].Magnetic Sensor measurement noises is 5nT, and accelerometer measures noise is 0.005m/s ², during initial attitude, terrestrial magnetic field is being projected as [35000 without magnetic regular hexahedron coordinate system;-33000;-2000] nT, gravity is being projected as [9.5 without magnetic regular hexahedron; 0.8; 0.5] m/s ².

Definition Magnetic Sensor coordinate system three axes is expressed as X _c, Y _c, Z _c; Accelerometer coordinate system three axes is expressed as X _g, Y _g, Z _g;

1, first, rotate around its X-axis without magnetic regular hexahedron, rotational angle is spaced apart 10 °, Magnetic Sensor X _caxle measured value is as table 1; Accelerometer X _gaxle measured value is as table 3;

2, secondly, rotate around its Z axis without magnetic regular hexahedron, rotational angle is spaced apart 10 °.Magnetic Sensor Z _caxle measured value is as table 1; Accelerometer Z _gaxle measured value is as table 3;

3, in measuring process, adopting sways measures mean value and to project reference value as rotation axis.Without magnetic regular hexahedron when its X-axis is rotated, Magnetic Sensor X _cthe measurement mean value of axle is 35005nT, accelerometer X _gthe measurement mean value of axle is 9.502m/s ².Without magnetic regular hexahedron when its Z axis rotates, Magnetic Sensor Z _cthe measurement mean value of axle is 34979nT, accelerometer Z _gthe measurement mean value of axle is 9.498m/s ².Due in actual mechanical process, be difficult to obtain terrestrial magnetic field and project without magnetic regular hexahedron coordinate system X-axis: 35000nT, emulation experiment is in order to closer to actual conditions, therefore the measurement mean value that use is swayed is as the actual value H that projects ^xand H ^zcarry out parameter estimation.

4, adopt formula (5) and formula (8) to carry out Solving Nonlinear Systems of Equations, calculate the non-aligned angle of Magnetic Sensor: [α _magβ _magγ _mag]=[0.4998 ° 0.8 ° 0.86 °], the non-aligned angular estimation error of known Magnetic Sensor is less than 5%.Equally, the non-aligned angle of accelerometer is calculated: [α _accβ _accγ _acc]=[0.596 ° 0.802 ° 1.12 °], known, evaluated error is less than 13%.Illustrate, non-aligned angular estimation precision is better.Next, adopt the non-aligned angle estimated, projection transform is carried out to measured value, thus assesses the calibration result of non-aligned angle to measured value.

5, according to the Magnetic Sensor calculated and without the non-aligned angle between magnetic regular hexahedron, Magnetic Sensor measured value can be transformed into magnetic field in the projection without magnetic regular hexahedron coordinate system.In theory, after being corrected by non-aligned angle, when rotating around its X-axis without magnetic regular hexahedron, Magnetic Sensor X-axis measured value comparison of coherence in rotation process is good, and should be 35000nT always; Measurement error before and after non-aligned correction is contrasted, the calibration result of non-aligned parameter can be assessed, Magnetic Sensor X _caxle measuring error is to such as table 2.Equally, when rotating around its Z axis without magnetic regular hexahedron, Magnetic Sensor Z _caxle measured value comparison of coherence in rotation process is good, and should be 35000nT always, Magnetic Sensor Z _caxle measuring error is to such as table 2.Known, Magnetic Sensor and without after correction non-aligned between magnetic regular hexahedron, the Magnetic Sensor of rotating shaft direction is measured consistance and is obviously improved, and closer to magnetic field in the real projection value without magnetic regular hexahedron, illustrates that the method can the effective non-aligned angle of estimated magnetic flux sensor.

The measurement data (rotating around X and Z axis respectively) of table 1 triaxial magnetic field sensor

The measuring error contrast (rotating around X and Z axis respectively) of table 2 triaxial magnetic field sensor

6, according to the accelerometer calculated and without the non-aligned angle between magnetic regular hexahedron, acceleration measuring value can be transformed into gravity in the projection without magnetic regular hexahedron coordinate system.In theory, after being corrected by non-aligned angle, when rotating around its X-axis without magnetic regular hexahedron, accelerometer X _gaxle measured value comparison of coherence in rotation process is good, and should be 9.5m/s always ²; Measurement error before and after non-aligned correction is contrasted, the calibration result of non-aligned parameter can be assessed, accelerometer X _gaxle measuring error is to such as table 4.Equally, when rotating around its Z axis without magnetic regular hexahedron, accelerometer Z _gaxle measured value comparison of coherence in rotation process is good, and should be 9.5m/s always ², accelerometer Z _gaxle measuring error is to such as table 4.Known, accelerometer and without after correction non-aligned between magnetic regular hexahedron, the accelerometer measures consistance of rotating shaft direction is obviously improved, closer to gravity in the real projection value without magnetic regular hexahedron, illustrates that the method can the effective non-aligned angle of estimated acceleration meter.

The measurement data (rotating around X and Z axis respectively) of table 3 three axis accelerometer

The measuring error contrast (rotating around X and Z axis respectively) of table 4 three axis accelerometer

Below be only the preferred embodiment of the present invention, protection scope of the present invention be not only confined to above-described embodiment, all technical schemes belonged under thinking of the present invention all belong to protection scope of the present invention.It should be pointed out that for those skilled in the art, some improvements and modifications without departing from the principles of the present invention, should be considered as protection scope of the present invention.

Claims (5)

1., based on the non-aligned bearing calibration of earth magnetism vector system around method of principal axes, it is characterized in that, comprise the following steps:

(S1) arrange without magnetic turntable, comprise a pedestal, a table top and a turning axle, described rotation axis vertically connects pedestal and table top;

(S2) by the Magnetic Sensor in earth magnetism vector measurement system and accelerometer package in without in magnetic regular hexahedron, if be XYZ without the coordinate of magnetic regular hexahedron;

(S3) be positioned on the table top without magnetic turntable by without magnetic regular hexahedron, keep consistent with turning axle direction without the X-direction of magnetic regular hexahedron, rotate and make to rotate unspecified angle without magnetic regular hexahedron around X-axis without magnetic turntable table top, the measured value of record Magnetic Sensor and accelerometer, rotates N around X-axis altogether ₁secondary, obtain N ₁the measured value of group Magnetic Sensor and accelerometer;

(S4) upset is without magnetic regular hexahedron, keep consistent with turning axle direction without the Z-direction of magnetic regular hexahedron, rotate and make to rotate unspecified angle without magnetic regular hexahedron around Z axis without magnetic turntable table top, the measured value of record Magnetic Sensor and accelerometer, rotates N around Z axis altogether ₂secondary, obtain N ₂the measured value of group Magnetic Sensor and accelerometer;

(S5) according to the N obtaining Magnetic Sensor and accelerometer ₁group and N ₂group measured value, according to the magnetic field on turning axle direction and weight component invariance principle, calculate respectively Magnetic Sensor to without the non-aligned angle of magnetic regular hexahedron and accelerometer to the non-aligned angle without magnetic regular hexahedron;

(S6) according to Magnetic Sensor to without the non-aligned angle of magnetic regular hexahedron and accelerometer to the non-aligned angle without magnetic regular hexahedron, determine the ordinate transform relation between Magnetic Sensor and accelerometer, namely complete correction.

2. a kind ofly as claimed in claim 1 to it is characterized in that based on the non-aligned bearing calibration of earth magnetism vector system around method of principal axes, according to the N of Magnetic Sensor and accelerometer in described step (S5) ₁group and N ₂group measured value, calculating Magnetic Sensor to the non-aligned angle detailed process of regular hexahedron is:

(S501) according to following formula, Magnetic Sensor measured value, field projection value and non-aligned angular dependence is set up:

$H^x=H_{\max }^{\mathrm{xx}}{a}_{11}+H_{\max }^{\mathrm{xy}}{a}_{21}+H_{\max }^{\mathrm{xz}}{a}_{31},$

$H^z=H_{\max }^{\mathrm{zx}}{a}_{13}+H_{\max }^{\mathrm{zy}}{a}_{23}+H_{\max }^{\mathrm{zz}}{a}_{33},$

Wherein, for without magnetic regular hexahedron Magnetic Sensor measured value when X-axis rotates, for without magnetic regular hexahedron Magnetic Sensor measured value when Z axis rotates; H ^xfor without magnetic regular hexahedron when X-axis rotates, terrestrial magnetic field is without magnetic regular hexahedron X-axis projection value; H ^zfor without magnetic regular hexahedron when Z axis rotates, terrestrial magnetic field is without magnetic regular hexahedron Z axis projection value; $\left\{\begin{array}{c}{a}_{11}=\cos {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\β}}_{\mathrm{mag}}\\ a_{21}=-\sin {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\β}}_{\mathrm{mag}}\\ a_{31}=\sin {\mathrm{\β}}_{\mathrm{mag}}\end{array}\right.,$ $\left\{\begin{array}{c}{a}_{13}=\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}-\cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ a_{23}=\cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}+\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ a_{33}=\cos {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\end{array}\right.,$ α _mag, β _mag, γ _magrepresent Magnetic Sensor and without the non-aligned angle between magnetic regular hexahedron;

(S502) according to following formula, N is utilized ₁group and N ₂group measured value calculates Magnetic Sensor and without the non-aligned angle α between magnetic regular hexahedron _mag, β _mag, γ _mag:

$\left\{\begin{array}{c}{H}^x=H_{\mathrm{mag}}^{\mathrm{xx}1}{a}_{11}+H_{\mathrm{mag}}^{\mathrm{xy}1}{a}_{21}+H_{\mathrm{mag}}^{\mathrm{xz}1}{a}_{31}\\ H^x=H_{\mathrm{mag}}^{\mathrm{xx}2}{a}_{11}+H_{\mathrm{mag}}^{\mathrm{xy}2}{a}_{21}+H_{\mathrm{mag}}^{\mathrm{xz}2}{a}_{31}\\ .\\ .\\ .\\ H^x=H_{\mathrm{mag}}^{\mathrm{xx}{N}_1}{a}_{11}+H_{\mathrm{mag}}^{\mathrm{xy}{N}_1}{a}_{21}+H_{\mathrm{mag}}^{\mathrm{xz}{N}_1}{a}_{31}\end{array}\right.$ With $\left\{\begin{array}{c}{H}^z=H_{\mathrm{mag}}^{\mathrm{zx}1}{a}_{13}+H_{\mathrm{mag}}^{\mathrm{zy}1}{a}_{23}+H_{\mathrm{mag}}^{\mathrm{zz}1}{a}_{23}\\ H^z=H_{\mathrm{mag}}^{\mathrm{zx}2}{a}_{13}+H_{\mathrm{mag}}^{\mathrm{zy}2}{a}_{23}+H_{\mathrm{mag}}^{\mathrm{zz}2}{a}_{33}\\ .\\ .\\ .\\ H^z=H_{\mathrm{mag}}^{\mathrm{zx}{N}_2}{a}_{13}+H_{\mathrm{mag}}^{\mathrm{zy}{N}_2}{a}_{23}+H_{\mathrm{mag}}^{\mathrm{zz}{N}_2}{a}_{33}\end{array}\right.;$

Wherein, , indicate without the magnetic regular hexahedron N that Magnetic Sensor exports when X-axis rotates ₁group measured value; , indicate without the magnetic regular hexahedron N that Magnetic Sensor exports when Z axis rotates ₂group measured value;

In described step (S5), calculating accelerometer to the detailed process at the non-aligned angle without magnetic regular hexahedron is:

(S511) according to following formula, acceleration measuring value, gravity projection value and non-aligned angular dependence is set up,

$g^x=g_m^{\mathrm{xx}}{b}_{11}+g_m^{\mathrm{xy}}{b}_{21}+g_m^{\mathrm{xz}}{b}_{31},$

$g^z=g_m^{\mathrm{zx}}{b}_{11}+g_m^{\mathrm{zy}}{b}_{23}+g_m^{\mathrm{zz}}{b}_{33},$

Wherein, for rotating brief acceleration measurement value without magnetic regular hexahedron around X-axis, for without magnetic regular hexahedron Magnetic Sensor measured value when Z axis rotates; g ^xfor without magnetic regular hexahedron when X-axis rotates, gravity is without magnetic regular hexahedron X-axis projection value; g ^zfor without magnetic regular hexahedron when Z axis rotates, gravity is without magnetic regular hexahedron Z axis projection value; $\left\{\begin{array}{c}{b}_{11}=\cos {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\β}}_{\mathrm{acc}}\\ b_{21}=-\sin {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\β}}_{\mathrm{acc}}\\ b_{31}=\sin {\mathrm{\β}}_{\mathrm{acc}}\end{array}\right.,$ $\left\{\begin{array}{c}{b}_{13}=\sin {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}-\cos {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\\ b_{23}=\cos {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}+\sin {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\\ b_{33}=\cos {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\end{array}\right.,$ α _acc, β _acc, γ _accfor accelerometer and without the non-aligned angle between magnetic regular hexahedron;

(S512) according to following formula, N is utilized ₁group and N ₂group measured value calculates accelerometer and without the non-aligned angle α between magnetic regular hexahedron _acc, β _acc, γ _acc:

$\left\{\begin{array}{c}{g}^x=g_m^{\mathrm{xx}1}{b}_{11}+g_m^{\mathrm{xy}1}{b}_{21}+b_m^{\mathrm{xz}1}{b}_{31}\\ g^x=g_m^{\mathrm{xx}2}{b}_{11}+H_m^{\mathrm{xy}2}{b}_{21}+H_m^{\mathrm{xz}2}{b}_{31}\\ .\\ .\\ .\\ g^x=g_m^{\mathrm{xx}{N}_1}{b}_{11}+H_m^{\mathrm{xy}{N}_1}{b}_{21}+H_m^{\mathrm{xz}{N}_1}{b}_{31}\end{array}\right.$ With $\left\{\begin{array}{c}{g}^z=g_m^{\mathrm{zx}1}{a}_{13}+g_m^{\mathrm{zy}1}{a}_{23}+g_m^{\mathrm{zz}1}{a}_{33}\\ g^z=g_m^{\mathrm{zx}2}{a}_{11}+g_m^{\mathrm{zy}2}{a}_{23}+g_m^{\mathrm{zz}2}{a}_{31}\\ .\\ .\\ .\\ g^z=g_m^{\mathrm{zxN}2}{a}_{13}+g_m^{\mathrm{zyN}2}{a}_{23}+g_m^{\mathrm{zzN}2}{a}_{33}\end{array}\right.$

Wherein, , indicate the N rotating the output of brief acceleration meter without magnetic regular hexahedron around X-axis ₁group measured value; , indicate the N rotating the output of brief acceleration meter without magnetic regular hexahedron around Z axis ₂group measured value.

3. a kind ofly as claimed in claim 2 it is characterized in that based on the non-aligned bearing calibration of earth magnetism vector system around method of principal axes, the detailed process of described step (S6) is:

(S61) according to α _mag, β _mag, γ _mag, realize Magnetic Sensor measured value be converted to magnetic field at the projection value without magnetic regular hexahedron computing formula is as follows:

$\left[\begin{array}{c}{B}_L^x\\ B_L^y\\ B_L^z\end{array}\right]=\left[\begin{array}{ccc}\cos {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\β}}_{\mathrm{mag}}& \sin {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}+\cos {\mathrm{\α}}_{\mathrm{mag}}{\mathrm{\β}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}& \sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}-\cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ -\sin {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\β}}_{\mathrm{mag}}& \cos {\mathrm{\α}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}-\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}& \cos {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}+\sin {\mathrm{\α}}_{\mathrm{mag}}\sin {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\\ \sin {\mathrm{\β}}_{\mathrm{mag}}& -\cos {\mathrm{\β}}_{\mathrm{mag}}\sin {\mathrm{\γ}}_{\mathrm{mag}}& \cos {\mathrm{\β}}_{\mathrm{mag}}\cos {\mathrm{\γ}}_{\mathrm{mag}}\end{array}\right]\·\left[\begin{array}{c}{H}_{\mathrm{mag}}^x\\ H_{\mathrm{mag}}^y\\ H_{\mathrm{mag}}^z\end{array}\right];$

(S62) according to α _acc, β _acc, γ _acc, realize be transformed into the field projection value of accelerometer coordinate system computing formula is as follows:

$\left[\begin{array}{c}{B}_{\mathrm{mag}}^x\\ B_{\mathrm{mag}}^y\\ B_{\mathrm{mag}}^z\end{array}\right]={\left[\begin{array}{ccc}\cos {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\β}}_{\mathrm{acc}}& \sin {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}+\cos {\mathrm{\α}}_{\mathrm{acc}}{\mathrm{\β}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}& \sin {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}-\cos {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\\ -\sin {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\β}}_{\mathrm{acc}}& \cos {\mathrm{\α}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}-\sin {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}& \cos {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}+\sin {\mathrm{\α}}_{\mathrm{acc}}\sin {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\\ \sin {\mathrm{\β}}_{\mathrm{acc}}& -\cos {\mathrm{\β}}_{\mathrm{acc}}\sin {\mathrm{\γ}}_{\mathrm{acc}}& \cos {\mathrm{\β}}_{\mathrm{acc}}\cos {\mathrm{\γ}}_{\mathrm{acc}}\end{array}\right]}^{-1}\·\left[\begin{array}{c}{B}_L^x\\ B_L^y\\ B_L^z\end{array}\right]$

Therefore, obtain the ordinate transform relation between Magnetic Sensor and accelerometer, namely complete correction.

4. a kind ofly as claimed in claim 1 it is characterized in that based on the non-aligned bearing calibration of earth magnetism vector system around method of principal axes, described Magnetic Sensor adopts magnetic sensor, and described accelerometer adopts three axis accelerometer.

5. a kind ofly as claimed in claim 1 it is characterized in that based on the non-aligned bearing calibration of earth magnetism vector system around method of principal axes, described is the regular hexahedron adopting plastic resin material to make without magnetic regular hexahedron.