CN109612471B - Moving body attitude calculation method based on multi-sensor fusion - Google Patents

Moving body attitude calculation method based on multi-sensor fusion Download PDF

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CN109612471B
CN109612471B CN201910107827.5A CN201910107827A CN109612471B CN 109612471 B CN109612471 B CN 109612471B CN 201910107827 A CN201910107827 A CN 201910107827A CN 109612471 B CN109612471 B CN 109612471B
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magnetometer
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CN109612471A (en
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邓志红
严丹
韩奋凯
王鹏宇
尚克军
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
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Abstract

The invention discloses a moving body attitude calculation method based on multi-sensor fusion, which comprises the steps of fixing a micro-electromechanical inertia and magnetic measurement unit on a carrier to be measured, collecting acceleration, angular rate and magnetic induction intensity, establishing a first-stage loss function according to a measurement model of an accelerometer, estimating a current attitude quaternion by using the acceleration through a gradient descent method, weighting the current attitude quaternion and an attitude quaternion updated through the angular rate to obtain a first-stage posterior attitude quaternion
Figure DDA0001967063430000011
By using
Figure DDA0001967063430000012
Updating a pitch angle and a roll angle of the carrier; under the condition of considering ferromagnetic interference, a second-stage loss function is established according to a measurement model of the magnetometer, the ferromagnetic interference estimator obtained by calculation at the previous moment and the magnetic induction intensity at the current moment are used for estimating the quaternion of the current attitude by a gradient descent method, and the quaternion of the second-stage posterior attitude is obtained by weighting the quaternion of the current attitude updated by the angular rate
Figure DDA0001967063430000013
By using
Figure DDA0001967063430000014
The invention can estimate the external ferromagnetic interference to realize the compensation of the ferromagnetic interference.

Description

Moving body attitude calculation method based on multi-sensor fusion
Technical Field
The invention belongs to the field of motion capture of micro-electromechanical inertial and magnetic measurement units (MIMMU), and particularly relates to a moving body attitude calculation method based on multi-sensor fusion.
Background
The attitude calculation system based on the micro-electromechanical inertia and magnetic measurement unit is widely applied to the fields of aircrafts, robots, human body motion capture and the like due to the characteristics of strong autonomy, high cost performance and small size. The inertia and magnetic measurement unit consists of a three-axis gyroscope, a three-axis accelerometer and a three-axis magnetometer and can be used for measuring the angular rate, the acceleration and the magnetic induction intensity of the carrier. Because the gyroscope has instantaneous drift, in the process of obtaining the carrier attitude by using angular rate integration, system errors can be accumulated along with time, and divergence is likely to be caused by long-time operation. The roll angle and the pitch angle of the carrier can be solved only by utilizing the gravity acceleration component under the carrier coordinate system, the course angle of the carrier can be solved by utilizing the earth magnetic field component under the carrier coordinate system, and the calculation of the roll angle and the pitch angle is only based on the current instantaneous data, so the error of the carrier does not accumulate along with time. Therefore, the inertial and Magnetic measurement units are used for realizing an algorithm for solving the carrier attitude jointly by information fusion based on Magnetic induction intensity, Angular Rate and Gravity acceleration (MARG) data, and the roll angle, the pitch angle and the course angle can be effectively corrected, so that the solving precision can be effectively improved, and the system can work for a long time. Compared with a Kalman filtering method, the MARG combined attitude measurement method based on the optimized compensation has smaller calculated amount and stronger robustness. However, the current optimization compensation algorithm does not consider the interference of external ferromagnetic substances to the magnetometer, and the algorithm cannot work normally when the ferromagnetic interference is large. In addition, the same filter is used for fusing MIMMU data, accelerometer data can cause adverse effects on the calculation of yaw angle, and magnetometer data can cause adverse effects on the calculation of roll angle and pitch angle.
Disclosure of Invention
In view of this, the invention provides a moving body attitude calculation method based on multi-sensor fusion, which can estimate external ferromagnetic interference so as to compensate the ferromagnetic interference and ensure that the algorithm can still be normally used in a complex environment.
The technical scheme for realizing the invention is as follows:
a moving body attitude calculation method based on multi-sensor fusion fixes a micro-electromechanical inertia and magnetic measurement unit (MIMMU) on a carrier to be measured, collects carrier acceleration, angular rate and magnetic induction intensity data, and establishes a first-stage loss function F according to a measurement model of the accelerometer1(. using acceleration data y)A，tEstimation of current attitude quaternion by gradient descent method
Figure GDA0003061338100000021
And compares it with the passing angular rate data yG，tUpdated attitude quaternion
Figure GDA0003061338100000022
Weighting to obtain first-stage posterior attitude quaternion
Figure GDA0003061338100000023
By using
Figure GDA0003061338100000024
Updating the pitch angle pitch of the carrierAAnd roll angle rollA(ii) a Establishing a second-order loss function F from a magnetometer's metrology model taking into account ferromagnetic interference2(. to) using the ferromagnetic interference estimate calculated at the previous time
Figure GDA0003061338100000025
And magnetic induction intensity data y at the current momentM，tEstimation of current attitude quaternion by gradient descent method
Figure GDA0003061338100000026
And compares it with the passing angular rate data yG，tUpdated attitude quaternion
Figure GDA0003061338100000027
Weighting to obtain a second-level posterior attitude quaternion
Figure GDA0003061338100000028
By using
Figure GDA0003061338100000029
Updating the yaw angle of the carrierM。
Further, the updated yaw angle yawMPitch angle pitchAAnd roll angle rollAConverted into attitude quaternions, i.e. posterior attitude quaternions at the present time
Figure GDA00030613381000000210
Magnetometer-based metrology model using a posteriori attitude quaternion
Figure GDA00030613381000000211
And magnetic induction data yM，tEstimation of ferromagnetic interference
Figure GDA00030613381000000212
And (6) updating.
Further, a second stage loss function F2(x)＝ε2(x)Tε2(x)，
Wherein the content of the first and second substances,
Figure GDA00030613381000000213
yM，tthe magnetic induction data measured by the magnetometer at the time t, d is ferromagnetic interference, q represents the carrier attitude,
Figure GDA00030613381000000214
representing the local earth magnetic field observed in the carrier coordinate system.
Has the advantages that:
1. the invention provides a two-stage attitude updating algorithm based on a gradient descent method, wherein the pitch angle and the roll angle are updated through the angular rate measured by a gyroscope and the acceleration data measured by an accelerometer in the first stage of filtering, and the yaw angle is updated through the angular rate measured by the gyroscope and the magnetic induction intensity data measured by a magnetometer in the second stage of filtering, so that the calculation precision of the system is improved.
2. Aiming at the problem that the magnetometer is easily interfered by external ferromagnetism, the algorithm estimates and compensates the ferromagnetism in real time in the second-stage filtering, so that the algorithm has certain ferromagnetism interference resistance, and the system can still normally work in a strong ferromagnetism interference environment.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
Aiming at the characteristics that accelerometer data can only be used for correcting roll angle and pitch angle, magnetometer data can be used for correcting yaw angle, but magnetometer is easily interfered by external ferromagnetism, the invention provides a two-stage updating algorithm based on gradient descent, in the first stage, gyroscope and accelerometer data are fused, and the pitch angle and roll angle of a carrier are updated; and in the second stage, the gyroscope and the magnetometer are subjected to data fusion, and the yaw angle of the carrier is updated. And estimating the external ferromagnetic interference in the second-stage algorithm to realize the compensation of the ferromagnetic interference and ensure that the algorithm can still be normally used in a more complex environment. The specific content of the invention comprises the following steps:
step 1: fixing a micro-electromechanical inertia and magnetic measurement unit (MIMMU) on a carrier to be measured, and collecting carrier acceleration, angular rate and magnetic induction intensity data;
a micro-electromechanical inertial and magnetic measurement unit (MIMMU) is fixed to a carrier to be measured. Let the carrier coordinate system ObxbybzbAttached to MIMMU at origin ObAt the MIMMU center of gravity, xbThe axis pointing to the right along the MIMMU horizontal axis, zbThe axis pointing upwards along the MIMMU vertical axis, ybAxis and xb、zbThe axes form a right-handed rectangular coordinate system. Setting a navigation coordinate system OnxnynznCoinciding with the carrier coordinate system at the initial instant. A gyroscope, an accelerometer and a magnetometer in the MIMMU respectively acquire angular rate, acceleration and magnetic induction intensity data of the carrier during motion and are used for subsequent carrier attitude calculation.
Step 2: establishing a first-order loss function F according to a measurement model of an accelerometer1(. using acceleration data y)A，tEstimation of current attitude quaternion by gradient descent method
Figure GDA0003061338100000041
And compares it with the passing angular rate data yG，tUpdated attitude quaternion
Figure GDA0003061338100000042
Weighting to obtain first-stage posterior attitude quaternion
Figure GDA0003061338100000043
By using
Figure GDA0003061338100000044
Updating the pitch angle pitch of the carrierAAnd roll angle rollA；
In the application scenario of the present invention, the motion acceleration measured in the carrier coordinate system is smaller than the gravity acceleration, so that the motion acceleration is ignored, and the accelerometer measurement model can be set as:
Figure GDA0003061338100000045
wherein, yA，tData measured by the accelerometer at time t; bAThe accelerometer represents a constant zero offset and can be corrected through data preprocessing; v. ofA，tRepresenting accelerometer noise as white gaussian noise; g is the local gravitational acceleration measured under the navigation coordinate system; q. q.stRepresenting a real attitude quaternion at the moment t;
Figure GDA0003061338100000046
is a rotation matrix from the navigation coordinate system to the carrier coordinate system:
Figure GDA0003061338100000047
thus, it is possible to provide
Figure GDA0003061338100000048
And represents the local gravity acceleration observed under the carrier coordinate system at the moment t.
the error between the actual measured value and the estimated value of acceleration at time t can be expressed as:
Figure GDA0003061338100000049
it can be known that the real attitude quaternion q is closer to the t moment when the attitude q of the carrier is closer to the t momenttWhen is equal to1The closer to [ 000 ] (q)]T. Using epsilon1The sum of the squares of the elements of (·) as a function of the first-order loss:
F1(q)＝ε1(q)Tε1(q) (4)
let the posterior attitude quaternion at the time of t-1 be
Figure GDA0003061338100000051
Using it as initial value of optimized q, and using gradient descent method to F1Optimization is performed to update the variables along the negative gradient direction of the loss function, which helps to reduce the value of the loss function:
Figure GDA0003061338100000052
wherein the content of the first and second substances,
Figure GDA0003061338100000053
an attitude quaternion updated for acceleration data measured by the accelerometer at time t; beta is a1For updating the step length, the step length is an adjustable parameter;
Figure GDA0003061338100000054
to represent
Figure GDA0003061338100000055
About
Figure GDA0003061338100000056
And solving the result of transposition after partial derivation.
From angular rate data y measured by a gyroscopeG，tUpdating the attitude quaternion differential equation to obtain the prior attitude quaternion
Figure GDA0003061338100000057
Figure GDA0003061338100000058
Wherein the content of the first and second substances,
Figure GDA0003061338100000059
and T is the sampling period of the gyroscope.
First order posterior attitude quaternion
Figure GDA00030613381000000510
Can be composed of
Figure GDA00030613381000000511
Weighted addition yields:
Figure GDA00030613381000000512
updated by acceleration data, due to the presence of motion acceleration objectively
Figure GDA00030613381000000513
With less confidence than updated by gyroscope data
Figure GDA00030613381000000514
Thus weighting the parameter mu1The value is smaller, (7) can be simplified as:
Figure GDA00030613381000000515
where ρ is1＝μ1β1Is an adjustable parameter.
Then will be
Figure GDA00030613381000000516
Euler angle [ yaw ] converted to "ZXY" rotation sequenceA pitchA rollA]。
And step 3: establishing a second-order loss function F from a magnetometer's metrology model taking into account ferromagnetic interference2(. to) using the ferromagnetic interference estimate calculated at the previous time
Figure GDA00030613381000000517
And magnetic induction intensity data y at the current momentM，tEstimation of current attitude quaternion by gradient descent method
Figure GDA00030613381000000518
And compares it with the passing angular rate data yG，tUpdated attitude quaternion
Figure GDA00030613381000000519
Weighting to obtain a second-level posterior attitude quaternion
Figure GDA00030613381000000520
By using
Figure GDA00030613381000000521
Updating the yaw angle of the carrierM；
Establishing a measurement model of the magnetometer:
Figure GDA0003061338100000061
wherein, yM，tData measured by the magnetometer at the time t; v. ofM，tMagnetometer noise, white gaussian noise;
Figure GDA0003061338100000062
the local earth magnetic field observed under the carrier coordinate system at the moment t is represented and is a part of a main body of data measured by the magnetometer; dtThe magnetometer represents ferromagnetic interference suffered by the magnetometer at the time t, is another part of the main body of the data measured by the magnetometer, and can be regarded as a random walk process according to the sequence of the time variation:
dt+1＝dt+wd，t (10)
wherein, wd，tIs gaussian white noise.
Because the intensity of the earth magnetic field on the earth surface is in the range of 25-65 mu T, the earth magnetic field is weak, the ferromagnetic interference value is often greater than the earth magnetic field, therefore, the ferromagnetic interference part can not be ignored, and the invention selects the ferromagnetic interference dtAnd (6) estimating.
The error between the actual measurement and the estimated value of the magnetometer at time t is given by equation (9):
Figure GDA0003061338100000063
it can be seen that the real value q of the quaternion is rotated as q gets closer to ttThe closer d is to the ferromagnetic disturbance d at time ttWhen is equal to2The closer to [ 000 ] the (q, d)]T。
Let x be [ q d ]]Using epsilon2The sum of the squares of the elements of (·) as a second-order loss function:
F2(x)＝ε2(x)Tε2(x) (12)
using gradient descent method to F2And (3) optimizing:
Figure GDA0003061338100000064
wherein the content of the first and second substances,
Figure GDA0003061338100000065
for time t passingA variable for magnetometer data update;
Figure GDA0003061338100000066
and
Figure GDA0003061338100000067
respectively the attitude quaternion and the estimated amount of ferromagnetic interference updated by the magnetic induction data at time t,
Figure GDA0003061338100000071
quaternion and ferromagnetic interference are estimated for the posteriori at time t-1; beta is a2To update the step size.
Second-order posterior attitude quaternion
Figure GDA0003061338100000072
Can be composed of
Figure GDA0003061338100000073
Weighted addition yields:
Figure GDA0003061338100000074
wherein the content of the first and second substances,
Figure GDA0003061338100000075
as a second-stage cost function
Figure GDA0003061338100000076
A posteriori estimated quaternion for time t-1
Figure GDA0003061338100000077
The result of transposing after partial derivation can be used for optimizing and estimating the quaternion. Data updating by magnetometers due to external ferromagnetic interference
Figure GDA0003061338100000078
With less confidence than updated by gyroscope data
Figure GDA0003061338100000079
Thus weighting the parameter mu2The value is smaller, (14) can be simplified as:
Figure GDA00030613381000000710
where ρ is2＝μ2β2Is an adjustable parameter.
Then will be
Figure GDA00030613381000000711
Euler angle [ yaw ] converted to "ZXY" rotation sequenceM pitchM rollM]。
And 4, step 4: will update the yaw angle yawMPitch angle pitchAAnd roll angle rollAConverted into attitude quaternions, i.e. posterior attitude quaternions at the present time
Figure GDA00030613381000000712
The pitch angle pitch obtained in step 2ARoll angle rollAYaw angle yaw obtained in step 3MCombined to form the Euler angle of posterior attitude [ yawM pitchA rollA]And converting the four-element number into an attitude quaternion, namely an a-posteriori attitude quaternion at the moment t
Figure GDA00030613381000000713
And 5: magnetometer-based metrology model using a posteriori attitude quaternion
Figure GDA00030613381000000714
And magnetic induction data yM，tEstimation of ferromagnetic interference
Figure GDA00030613381000000715
And updating for use in step 3 at the next time.
According to magnetometer measurement model(9) Using quaternion of a posterior attitude
Figure GDA00030613381000000716
And magnetometer data y at the present momentM，tAnd updating the posterior ferromagnetic estimation at the time t:
Figure GDA00030613381000000717
in summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (2)

1. A moving body attitude calculation method based on multi-sensor fusion is characterized in that a micro-electromechanical inertia and magnetic measurement unit is fixed on a carrier to be measured, and carrier acceleration, angular rate and magnetic induction intensity data are collected; establishing a first-order loss function F according to a measurement model of an accelerometer1(. using acceleration data y)A，tEstimation of current attitude quaternion by gradient descent method
Figure FDA0003061338090000011
And compares it with the passing angular rate data yG，tUpdated attitude quaternion
Figure FDA0003061338090000012
Weighting to obtain first-stage posterior attitude quaternion
Figure FDA0003061338090000013
By using
Figure FDA0003061338090000014
Updating the pitch angle pitch of the carrierAAnd roll angle rollA(ii) a Establishing a second metrology model from the magnetometer taking into account the ferromagnetic interferenceStage loss function F2(. to) using the ferromagnetic interference estimate calculated at the previous time
Figure FDA0003061338090000015
And magnetic induction intensity data y at the current momentM，tEstimation of current attitude quaternion by gradient descent method
Figure FDA0003061338090000016
And compares it with the passing angular rate data yG，tUpdated attitude quaternion
Figure FDA0003061338090000017
Weighting to obtain a second-level posterior attitude quaternion
Figure FDA0003061338090000018
By using
Figure FDA0003061338090000019
Updating the yaw angle of the carrierM；
Will update the yaw angle yawMPitch angle pitchAAnd roll angle rollAConverted into attitude quaternions, i.e. posterior attitude quaternions at the present time
Figure FDA00030613380900000110
Magnetometer-based metrology model using a posteriori attitude quaternion
Figure FDA00030613380900000111
And magnetic induction data yM，tEstimation of ferromagnetic interference
Figure FDA00030613380900000112
And (6) updating.
2. The multi-sensor fusion-based moving body attitude solution method according to claim 1, wherein the secondStage loss function F2(x)＝ε2(x)Tε2(x)，
Wherein x is [ q d ]]，
Figure FDA00030613380900000113
yM，tThe magnetic induction data measured by the magnetometer at the time t, d is ferromagnetic interference, q represents the carrier attitude,
Figure FDA00030613380900000114
representing the local earth magnetic field observed in the carrier coordinate system.
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