CN109084756B - Gravity apparent motion parameter identification and accelerometer zero-offset separation method - Google Patents

Gravity apparent motion parameter identification and accelerometer zero-offset separation method Download PDF

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CN109084756B
CN109084756B CN201810635511.9A CN201810635511A CN109084756B CN 109084756 B CN109084756 B CN 109084756B CN 201810635511 A CN201810635511 A CN 201810635511A CN 109084756 B CN109084756 B CN 109084756B
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CN109084756A (en
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刘锡祥
汪宋兵
郭小乐
黄荣
王启明
杨文强
许广富
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Southeast University
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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
    • G01C21/10—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
    • G01C21/16—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 by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/165—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 by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • 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
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices

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Abstract

The invention discloses a gravity apparent motion parameter identification and accelerometer zero-offset separation method, which comprises the following steps: constructing a gravity apparent motion/accelerometer zero-offset coupling model based on the gravity apparent motion; constructing an accelerometer zero-offset separation and parameter identification model; using obtained observations
Figure DDA0001701419170000011
Selecting a state vector of a system; and performing gravity apparent motion parameter identification and accelerometer zero offset separation through Kalman filtering. By adopting the gravity apparent motion parameter identification and accelerometer zero-offset separation method provided by the application, the gravity apparent motion parameter identification and accelerometer zero-offset separation are carried out under the conditions of zero speed and shaking of the base, the reconstructed gravity apparent motion is utilized for analysis and alignment, and the horizontal attitude angle error of the carrier approaches to a zero value.

Description

Gravity apparent motion parameter identification and accelerometer zero-offset separation method
Technical Field
The invention relates to a gravity apparent motion parameter identification and accelerometer zero-offset separation method, and belongs to the technical field of navigation algorithms.
Background
An inertial navigation system is a navigation system based on an integral working mode, and instrument errors are accumulated in the integral process, so that the system positioning errors rapidly increase along with the time. The instrument error, especially the constant zero offset of the gyroscope and the accelerometer, is considered to be a key factor determining the accuracy of the system. Initial alignment, including instrument error estimation, is often required prior to system navigation operations.
The system working site does not generally have external high-precision turntable equipment, and is often dependent on system-level calibration. The system level calibration needs to refer to external high-precision navigation information, wherein the speed is the most common and easily-obtained external reference information, such as zero-speed constraint in zero-speed correction, GNSS auxiliary speed in a GNSS/SINS combination and the like. The accelerometer zero offset integral is expressed as a speed error, and the accelerometer zero offset can be obtained through inversion according to the speed error. However, in the system-level calibration process based on velocity matching, there is coupling between the accelerometer zero offset and the INS horizontal misalignment angle, and there is coupling between the east gyroscope error, the north accelerometer zero offset, and the INS azimuth misalignment angle. Decoupling the above errors places additional requirements on the mobility of the vehicle. Such as ships, vehicles, large-scale flight, etc., which can not carry out the muscle fight and large-scale maneuvering motion of fighters. The calibration of the zero offset of the accelerometer is still difficult to accomplish without additional requirements on the maneuverability of the vehicle.
In addition, if the carrier shakes or (and) the navigation system/carrier system are not coincident, since the projection of the accelerometer in the carrier system, which is zero offset, in the navigation system cannot be determined, the accelerometer cannot be calibrated directly by using a comparison method, and a new approach is needed.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to find a zero offset calibration method of an accelerometer by only utilizing zero-speed constraint of a carrier and excitation of self-shaking on errors, such as ship swinging motion under the excitation of wind waves, and the like, on the premise of not providing additional requirements on the maneuverability of the carrier.
The technical scheme is as follows: the invention provides the following technical scheme:
a gravity apparent motion parameter identification and accelerometer zero offset separation method comprises the following steps:
1) establishing a gravity apparent motion and accelerometer zero-offset coupling model based on the gravity apparent motion;
2) constructing an accelerometer zero-offset separation and parameter identification model;
3) using obtained observations
Figure BDA0001701419150000021
Selecting a state vector of a system;
4) and performing gravity apparent motion parameter identification and accelerometer zero offset separation through Kalman filtering.
Further, the step 1) of constructing the gravity apparent motion/accelerometer zero-offset coupling model based on the gravity apparent motion specifically includes the following steps:
under the condition that the carrier has no linear motion, the theoretical vector measured by the accelerometer is the projection of the gravity vector under a carrier system b, and the expression form of the apparent motion of the gravity is given by using the projection of the measured value of the accelerometer under an inertial system as follows:
Figure BDA0001701419150000022
wherein i is an inertial coordinate system in0Navigation coordinate system as initial time, e0An earth coordinate system as an initial time, an earth coordinate system as a current time,
Figure BDA0001701419150000023
Representing a posture conversion matrix from B to A; in each of the above-described attitude matrices,
Figure BDA0001701419150000024
and
Figure BDA0001701419150000025
are all constant value matrices; when the carrier is moving wirelessly
Figure BDA0001701419150000026
Is also a constant value;
Figure BDA0001701419150000027
is a matrix related to time and the rotational angular velocity of the earth;
substituting the determined values with constants and developing the above equation, there are:
Figure BDA0001701419150000028
in the formula, a11～a33、b11～b33、c11～c33And A11～A33Are all constant values; omegaieG is the value of the rotational angular velocity and the gravitational acceleration of the earth respectively; t is the observation time length;
when the initial time carrier coordinate system is selected as the inertial system, the inertial system i can be defined as ib0The gravity apparent motion can be obtained by calculation according to the measurement values of the accelerometer and the gyroscope, and the specific calculation formula is as follows:
Figure BDA0001701419150000029
in the formula (3), the reaction mixture is,
Figure BDA0001701419150000031
calculated value for gravity-based motion,
Figure BDA0001701419150000032
Is an attitude matrix between the current time carrier system and the initial time carrier system,
Figure BDA0001701419150000033
Is an accelerometer measurement; wherein
Figure BDA0001701419150000034
Can be obtained by integrating a gyro, and the calculation formula is as follows:
Figure BDA0001701419150000035
considering the accelerometer constant zero offset and random noise, the accelerometer measurement model can be expressed as follows:
Figure BDA0001701419150000036
in the formula +bAnd ηbRespectively carrying out constant zero offset and random noise on the accelerometer; bringing equation (5) into equation (3) and ignoring gyroscope measurement errors, there are:
Figure BDA0001701419150000037
further, the step 2) of constructing the accelerometer zero-offset separation and parameter identification model specifically includes:
true value of gravity apparent motion
Figure BDA0001701419150000038
The reconstructed apparent gravity motion value can be used instead, i.e. formula (2) is substituted into formula (6), with:
Figure BDA0001701419150000039
in the formula C11～33Is a matrix
Figure BDA00017014191500000310
A corresponding element;
Figure BDA00017014191500000311
is ^bThe component of each axis under the carrier system b;
Figure BDA00017014191500000312
is composed of
Figure BDA00017014191500000313
At ib0Is tied to each shaftQuantity, random noise; equation (9) formally separates the gravitational apparent motion from the accelerometer zero offset, if A can be estimated in some form11～A33And
Figure BDA00017014191500000314
the decoupling of the gravity-dependent motion parameter identification and the acceleration zero offset can be realized.
Further, the step 3) utilizes the obtained observed quantity
Figure BDA00017014191500000315
Selecting a state vector of a system, specifically comprising:
using obtained observations
Figure BDA0001701419150000041
Estimating an optimal parameter; get A11～A33And
Figure BDA0001701419150000042
is a state vector, i.e.
Figure BDA0001701419150000043
From the above analysis, it can be seen that A is the moment when the inertial system is determined11～A33Is a fixed value. .
Further, the step 4) of performing gravity apparent motion parameter identification and accelerometer zero offset separation by Kalman filtering specifically comprises:
A11～A33for a fixed value, the quantity is considered constant in a short time, so that the system state equation is:
Xk＝Xk-1 \*MERGEFORMAT(9)
taking gravity as measured value, i.e.
Figure BDA0001701419150000044
According to equation (7), there is a measurement matrix:
Figure BDA0001701419150000045
in the formula C11～33Is a matrix
Figure BDA0001701419150000046
The elements in (1) and (14) form a system state equation and a measurement equation. Based on the equation, the estimation of the state quantity can be carried out by adopting a recursive least square method based on a Kalman filtering form; the recursive least squares based on-line identification filter can be constructed as follows:
Figure BDA0001701419150000047
in the formula, K represents the number of calculations, K represents the filter gain, P represents the error covariance, R represents the measurement error, and I represents the identity matrix.
Compared with the prior art, the invention has the beneficial effects that: by using the gravity apparent motion parameter identification and accelerometer zero-offset separation method provided by the application, under the conditions of zero speed and shaking of the base, the gravity apparent motion parameter identification and accelerometer zero-offset separation are carried out, the reconstructed gravity apparent motion is utilized to carry out analysis and alignment, the horizontal attitude angle error of the carrier is close to a zero value, and the method is characterized in that:
1) in the initial alignment process, no additional requirement is put on the mobility of the carrier;
2) in the alignment process, the carrier only utilizes zero-speed constraint, self-shaking and other external excitations;
3) combining a recursion algorithm with a least square method, and estimating the state quantity by applying a Kalman filtering form-based recursion least square method;
4) in the alignment process, the accelerometer constant zero offset can be calibrated and used for navigation calculation of SINS or other equipment.
Drawings
FIG. 1 is a schematic view of the gravity-based motion used in the present invention;
FIG. 2 is a diagram of the zero offset estimation result of the accelerometer under the condition of shaking the base according to the present invention;
FIG. 3 is a diagram showing the alignment result of the shaking base according to the present invention.
Detailed Description
The technical solution of the present invention is described in detail below, but the scope of the present invention is not limited to the embodiments.
Examples
The invention constructs a gravity apparent motion/accelerometer zero-offset coupling model based on the gravity apparent motion in an inertial system, then constructs an accelerometer zero-offset separation and parameter identification model, and utilizes the obtained observed quantity
Figure BDA0001701419150000051
And selecting a state vector of the system, and performing gravity apparent motion parameter identification and accelerometer zero offset separation through Kalman filtering.
The method of carrying out the invention is described in more detail below with reference to the accompanying drawings:
fig. 1 is a schematic diagram of the gravity-based motion used in the present invention, in which the change of the direction and magnitude of the gravitational acceleration at a certain point of the earth's rotation is observed in the inertial system to form the cone.
The method for constructing the gravity apparent motion/accelerometer zero-offset coupling model based on the gravity apparent motion specifically comprises the following steps:
under the condition that the carrier has no linear motion, the theoretical vector measured by the accelerometer is the projection of the gravity vector under a carrier system b, and the expression form of the apparent motion of the gravity is given by using the projection of the measured value of the accelerometer under an inertial system as follows:
Figure BDA0001701419150000052
wherein i is an inertial coordinate system in0Navigation coordinate system as initial time, e0Global coordinate system as initial time, e as current timeThe terrestrial coordinate system,
Figure BDA0001701419150000061
Representing the attitude transformation matrix from B to a. In each of the above-described attitude matrices,
Figure BDA0001701419150000062
and
Figure BDA0001701419150000063
are all constant value matrices; when the carrier is moving wirelessly
Figure BDA0001701419150000064
Is also a constant value;
Figure BDA0001701419150000065
is a matrix related to time and rotational angular velocity of the earth. Substituting the determined values with constants and developing the above equation, there are:
Figure BDA0001701419150000066
in the formula, a11～a33、b11～b33、c11～c33And A11～A33Are all constant values; omegaieG is the value of the rotational angular velocity and the gravitational acceleration of the earth respectively; t is the observation time length.
When the initial time carrier coordinate system is selected as the inertial system, the inertial system i can be defined as ib0The gravity apparent motion can be obtained by calculation according to the measurement values of the accelerometer and the gyroscope, and the specific calculation formula is as follows:
Figure BDA0001701419150000067
in the formula (3), the reaction mixture is,
Figure BDA0001701419150000068
calculated value for gravity-based motion,
Figure BDA0001701419150000069
Is an attitude matrix between the current time carrier system and the initial time carrier system,
Figure BDA00017014191500000610
Is an accelerometer measurement. Wherein
Figure BDA00017014191500000611
Can be obtained by integrating a gyro, and the calculation formula is as follows:
Figure BDA00017014191500000612
considering the accelerometer constant zero offset and random noise, the accelerometer measurement model can be expressed as follows:
Figure BDA00017014191500000613
in the formula +bAnd ηbAccelerometer constant zero offset and random noise, respectively. Bringing equation (5) into equation (3) and ignoring gyroscope measurement errors, there are:
Figure BDA00017014191500000614
Figure BDA0001701419150000071
the method for constructing the accelerometer zero-offset separation and parameter identification model specifically comprises the following steps:
true value of gravity apparent motion
Figure BDA0001701419150000072
The reconstructed apparent gravity motion value can be used instead, i.e. formula (2) is substituted into formula (6), with:
Figure BDA0001701419150000073
\*MERGEFORMAT(7)
in the formula C11～33Is a matrix
Figure BDA0001701419150000074
A corresponding element;
Figure BDA0001701419150000075
is ^bThe component of each axis under the carrier system b;
Figure BDA0001701419150000076
is composed of
Figure BDA0001701419150000077
At ib0Each axis component is random noise. Equation (9) formally separates the gravitational apparent motion from the accelerometer zero offset, if A can be estimated in some form11～A33And
Figure BDA0001701419150000078
the decoupling of the gravity-dependent motion parameter identification and the acceleration zero offset can be realized.
Using obtained observations
Figure BDA0001701419150000079
Selecting a state vector of a system, specifically comprising:
using obtained observations
Figure BDA00017014191500000710
The optimal parameters are estimated. Get A11～A33And
Figure BDA00017014191500000711
is a state vector, i.e.
Figure BDA00017014191500000712
When the inertial system has been determined, A11～A33Is a fixed value.
The gravity apparent motion parameter identification and accelerometer zero-offset separation through Kalman filtering specifically comprises the following steps:
A11～A33for a fixed value, the quantity is considered constant in a short time, so that the system state equation is:
Xk＝Xk-1 \*MERGEFORMAT(9)
taking gravity as measured value, i.e.
Figure BDA00017014191500000713
According to equation (7), there is a measurement matrix:
Figure BDA0001701419150000081
in the formula C11～33Is a matrix
Figure BDA0001701419150000083
The elements in (1) and (14) form a system state equation and a measurement equation. Based on the above equation, the estimation of the above state quantities can be performed by using a recursive least square method based on a Kalman filtering form. The online identification filter based on Kalman filtering form recursive least squares can be constructed as follows:
Figure BDA0001701419150000082
in the formula, K represents the number of calculations, K represents the filter gain, P represents the error covariance, R represents the measurement error, and I represents the identity matrix.
The beneficial effects of the invention are verified by the following simulation experiments:
matlab simulation condition setting
The ship is in a zero-speed shaking state, and the shaking motion of the ship obeys Asin (2 pi f.t + beta)0)+θ0Where A is the amplitude of the wobble, f is the frequency of the wobble, β0Is the initial phase angle, θ0Is the initial attitude angle of the ship relative to the navigation coordinate system. The relevant parameter settings are shown in the following table. The initial longitude and latitude of the ship are respectively 118 degrees of east longitude and 32 degrees of north latitude.
TABLE 1 rocking parameter settings
Pitching Roll and shake Course of course
Amplitude of oscillation (°) 6 13 8
Swing period(s) 10 8 8
Initial phase (°) 0 0 0
Initial angle (°) 2 6 5
And generating ideal data of the accelerometer and the gyroscope by utilizing a reverse navigation algorithm according to the motion rule. Adding the constant error and random error of the instrument to the ideal instrument data to generate the instrument data with errors for simulating the data output by the actual instrument, wherein the frequency of the instrument data generation is 100 Hz. The error parameter settings for the accelerometer and gyroscope are shown in table 2, where the random noise satisfies the white noise assumption.
TABLE 2 Instrument error settings
Figure BDA0001701419150000091
Verification of alignment and tabulation zero offset estimates
And carrying out algorithm verification on a common PC. Performing simulation for 4000s, wherein in the simulation process, (1) instrument data are generated; (2) calculating the gravity apparent motion by using the measurement values of the gyroscope and the accelerometer; (3) performing gravity apparent motion parameter identification accelerometer zero-offset separation through Kalman filtering; (4) analyzing and aligning by using the reconstructed gravity apparent motion; (5) and repeating the steps. Fig. 2 and 3 show the accelerometer constant zero offset error and the alignment result, respectively.
Fig. 2 shows the accelerometer constant zero offset estimate under the shaking, wireless motion base condition, where the solid line represents the error estimate and the dashed line represents the true error value. The curve shows that under the conditions of shaking and wireless motion, the zero offset of the three-axis accelerometer can be mostly estimated, and the error between the estimation result and the true value is small;
fig. 3 shows the alignment result obtained by reconstructing the gravity apparent motion and analyzing the alignment method using the gravity apparent motion identification parameter, wherein the dotted line represents the alignment result of the strapdown compass initial alignment method (method 1) based on the inertial system gravity apparent motion, the solid line represents the alignment result (method 2) after the separation accelerometer is zero offset, ideal eP, ideal eR and ideal eH are simultaneously plotted in the figure, the sublist represents the theoretical alignment accuracy values of the pitch angle, the roll angle and the heading angle, and the zero line zero is plotted. The curve shows that the horizontal alignment precision of the gravity apparent motion calculated value is greatly improved after the separation accelerometer is normally zero offset, and the error of the horizontal misalignment angle can approach zero.
As noted above, while the present invention has been shown and described with reference to certain preferred embodiments, it is not to be construed as limited thereto. Various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (3)

1. A gravity apparent motion parameter identification and accelerometer zero offset separation method is characterized by comprising the following steps:
1) constructing a gravity apparent motion and accelerometer zero-offset coupling model based on the gravity apparent motion;
2) constructing an accelerometer zero-offset separation and parameter identification model;
3) using obtained observations
Figure FDA0003135640270000011
Selecting a state vector of a system;
4) performing gravity apparent motion parameter identification and accelerometer zero-offset separation through Kalman filtering;
the step 1) specifically comprises the following steps:
under the condition that the carrier has no linear motion, the theoretical vector measured by the accelerometer is the projection of the gravity vector under a carrier system b, and the expression form of the apparent motion of the gravity is given by using the projection of the measured value of the accelerometer under an inertial system as follows:
Figure FDA0003135640270000012
wherein i is an inertial coordinate system in0Navigation coordinate system as initial time, e0Earth as an initial momentA coordinate system, e is a global coordinate system of the current time,
Figure FDA0003135640270000013
Representing a posture conversion matrix from B to A; in each of the above-described attitude matrices,
Figure FDA0003135640270000014
and
Figure FDA0003135640270000015
are all constant value matrices; when the carrier is moving wirelessly
Figure FDA0003135640270000016
Is also a constant value;
Figure FDA0003135640270000017
is a matrix related to time and the rotational angular velocity of the earth;
substituting the determined values with constants and developing the above equation, there are:
Figure FDA0003135640270000018
in the formula, a11～a33、b11～b33、c11～c33And A11～A33Are all constant values; omegaieG is the value of the rotational angular velocity and the gravitational acceleration of the earth respectively; t is the observation time length;
when the carrier coordinate system at the initial moment is selected as the inertia system, defining the inertia system i as ib0The gravity apparent motion is obtained by calculation according to the measurement values of the accelerometer and the gyroscope, and the specific calculation formula is as follows:
Figure FDA0003135640270000021
in the formula (3), the reaction mixture is,
Figure FDA0003135640270000022
calculated value for gravity-based motion,
Figure FDA0003135640270000023
Is an attitude matrix between the current time carrier system and the initial time carrier system,
Figure FDA0003135640270000024
Is an accelerometer measurement; wherein
Figure FDA0003135640270000025
Obtained by integrating with a gyroscope, the calculation formula is as follows:
Figure FDA0003135640270000026
considering the accelerometer constant zero offset and random noise, the accelerometer measurement model is expressed as follows:
Figure FDA0003135640270000027
in the formula (I), the compound is shown in the specification,
Figure FDA0003135640270000028
and ηbRespectively, accelerometer constant zero offset and random noise; bringing equation (5) into equation (3) and ignoring gyroscope measurement errors, there are:
Figure FDA0003135640270000029
the step 2) specifically comprises the following steps:
true value of gravity apparent motion
Figure FDA00031356402700000210
Substitution with the reconstructed apparent gravity motion value, i.e., substituting equation (2) into equation (6), has:
Figure FDA00031356402700000211
in the formula C11～33Is a matrix
Figure FDA00031356402700000212
A corresponding element;
Figure FDA00031356402700000213
is composed of
Figure FDA00031356402700000214
The component of each axis under the carrier system b;
Figure FDA00031356402700000215
is composed of
Figure FDA00031356402700000216
At ib0Is the random noise of each axis component; equation (7) formally separates the gravitational apparent motion from the accelerometer zero-bias, if A can be estimated in some form11～A33And
Figure FDA00031356402700000217
the decoupling of the gravity-dependent motion parameter identification and the acceleration zero offset is realized.
2. The method as claimed in claim 1, wherein the step 3) utilizes the obtained observed quantity
Figure FDA00031356402700000218
Selecting a state vector of a system, specifically comprising:
using obtained observations
Figure FDA00031356402700000219
Estimating an optimal parameter; get A11～A33And
Figure FDA00031356402700000220
is a state vector, i.e.
Figure FDA0003135640270000031
From the above analysis, it can be seen that A is the moment when the inertial system is determined11～A33Is a fixed value.
3. The method for identifying and separating zero offset of gravity-based motion parameters and accelerometer according to claim 1, wherein the step 4) of performing the zero offset separation of the gravity-based motion parameters and the accelerometer through Kalman filtering specifically comprises:
A11～A33for a fixed value, the quantity is constant for a short time, so that the system state equation is:
Xk＝Xk-1 (9)
taking gravity as measured value, i.e.
Figure FDA0003135640270000032
According to equation (7), there is a measurement matrix:
Figure FDA0003135640270000033
in the formula C11～33Is a matrix
Figure FDA0003135640270000034
Wherein the elements of formulas (9) to (11) constituteA system state equation and a measurement equation; based on the equation, estimating the state vector by adopting a recursive least square method based on a Kalman filtering form; the online identification filter based on recursive least squares is constructed as follows:
Figure FDA0003135640270000035
in the formula, K represents the number of calculations, K represents the filter gain, P represents the error covariance, R represents the measurement error, and I represents the identity matrix.
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