CN109827571A - A kind of dual acceleration meter calibration method under the conditions of no turntable - Google Patents
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Abstract
The invention discloses the dual acceleration meter calibration methods under the conditions of a kind of no turntable, at least there are two accelerometers in carrier inertial navigation system, it is referred to as accelerometer 1 and accelerometer 2, carrier inertial navigation system is placed in stationary state first, the described method includes: constructing and defining 2 zero offset error peg model of accelerometer 1 and accelerometer, while obtaining the error measurement vector in error calibration model;Accelerometer 1 and 2 zero offset error peg model of accelerometer are filtered with kalman filtering method, it is inputted error observation vector as filtering, three axis of the k moment output zero offset error calibration value of accelerometer 1 and accelerometer 2 is obtained from the convergence process to filtering, the present invention realizes the accurate On-line Estimation to accelerometer bias on the basis of obtaining inertial navigation system velocity error, in conjunction with kalman filtering technique.
Description
Technical field
The present invention relates to inertial navigation positioning fields, and in particular to the dual acceleration meter calibration side under the conditions of a kind of no turntable
Method is the accelerometer scaling method for being suitable for being mounted with two or more accelerometer platform under the conditions of a kind of no turntable.
Background technique
Inertial technology is the general designation to inertial guidance, inertial navigation and inertial survey technique, theoretical basis be built upon through
On allusion quotation mechanics law.Wherein, inertial navigation is such a special kind of skill, can once be found out to accelerometer output integral
Speed, integral can find out change in location twice, and direction and the size of rotation are determined with the measured value of gyroscope.By to top
The combined use of spiral shell instrument and accelerometer just can determine that the position of carrier.Inertial navigation need only obtain carrier accurately just
Or else beginning position introduces under the conditions of any external information, so that it may realize independent navigation later.For inertial navigation system
Speech determines that the central factor of its navigation accuracy is Inertial Measurement Unit (IMU, Inertial Measurement Unit) (general
Refer to gyroscope and accelerometer) measurement accuracy, how effectively to promote the measurement accuracy of IMU is always grinding for inertial navigation field
Study carefully emphasis.
The approach for improving IMU measurement accuracy can be divided into two classes: on the one hand by improving inertial sensor structures, improve processing
Technique improves device itself precision, optimizes Design of Mechanical Structure, improves the performance of electronic circuit, shields external electromagnetic interference, from
And improve measurement accuracy.Another aspect application error model analysis, software compensation technique, by error calibration and compensation technique come
The measurement accuracy of IMU is promoted as far as possible.And from the angle of engineer application, realize that error calibration is more feasible using algorithm
Method, can not only fully play the performance of device, in a sense, also reducing the cost of IMU.The calibration of IMU is
It is completed by being compared to known input motion and to its (IMU) analog or digital signal generated.To gyroscope
Calibration in, be that turntable gives the accurate speed of rotation using method, then given with the output signal of gyroscope and turntable
Fixed pumping signal comparison.The calibration of accelerometer is similar therewith, but given pumping signal is local gravitational vectors.
The accelerometer scaling method of comparative maturity is mainly multiposition scaling scheme (such as six location position sides at present
Method, nine position calibration methods etc.), this scheme is widely used in engineering, there is higher stated accuracy, core
Thought is want, in the case where accelerometer is in static, using gravitational vectors as driving source, to accelerate by turntable multiple rotary
Degree meter position is to realize that the accelerometer data under multiposition acquires, to complete the estimation of accelerometer bias.But it is this
The use condition of method is comparatively harsh, it is necessary first to which a turntable with certain precision is as reference data, it is ensured that more
Secondly opposite transformational relation between position is it is known that when needing to carry out long in the case where different location to the same accelerometer
Between data sampling;The two use conditions (especially to the demand of the turntable with certain precision) significantly limit this method
Extensive use in engineering.
Summary of the invention
The present invention proposes the dual acceleration meter calibration method under the conditions of a kind of no turntable, to realize the mark to accelerometer
It is fixed.
To achieve the goals above, the technical scheme is that
A kind of dual acceleration meter calibration method under the conditions of no turntable, is in carrier inertial navigation system to accelerometer
Carry out online error calibration, at least there are two accelerometer in carrier inertial navigation system, be referred to as accelerometer 1 and plus
Carrier inertial navigation system is placed in stationary state first by speedometer 2, which comprises
2 zero offset error peg model of accelerometer 1 and accelerometer is constructed and defined, while being obtained in error calibration model
Error measurement vector;
Accelerometer 1 and 2 zero offset error peg model of accelerometer are filtered with kalman filtering method, by error
Observation vector as filtering input, miss by three axis of the k moment output zero bias that accelerometer 1 is obtained from the convergence process to filtering
Three axis of k moment of difference and accelerometer 2 exports zero offset error;
Using three axis of k moment of accelerometer 1 and accelerometer 2 output zero offset error numerical value as calibration value, calibration is completed.
Scheme is further: described the step of constructing and defining 2 zero offset error peg model of accelerometer 1 and accelerometer
It is:
Step 1: being calculated by the three axis output of the accelerometer 1 and accelerometer 2 of acquisition stationary state moment k quiet
The only roll angle and pitch angle initial value of the roll angle of the accelerometer 1 of state and pitch angle initial value and accelerometer 2;
When the XYZ axis of carrier coordinate system corresponds respectively to the right front upper of carrier, the XYZ axis of navigational coordinate system is local east
When northern day:
Its calculation formula is respectively as follows:
Wherein:
It respectively representsIn carrier system X, Y, the projection on Z axis;
It respectively representsIn carrier system X, Y, the projection on Z axis;
WithIt is to be exported by 1 three axis of accelerometer respectivelyThe roll angle and pitching angle value being calculated;
WithIt is to be exported by 2 three axis of accelerometer respectivelyThe roll angle and pitching angle value being calculated;
Atan represents arctan function, and asin represents arcsin function;
G represents local gravitational acceleration;
Step 2: passing through the course angle true value for setting the k moment as ψk=0, it usesAnd ψkIt is defeated to construct accelerometer 1
Out carrier coordinate system to navigational coordinate system pose transformation matrixAnd it usesAnd ψkAccelerometer 2 is constructed to export
Carrier coordinate system to navigational coordinate system pose transformation matrix
Step 3: defining 2 zero offset error peg model of accelerometer 1 and accelerometer using pose transformation matrix:
X (k+1)=Akx(k)+ω
Z (k)=Hkx(k)+υ
Wherein:
It is the error state vector of accelerometer 1 and accelerometer 2 at the k moment,
a1=[a1(x) a1(y) a1(z)]TIt is 1 three axis zero offset error of accelerometer;
a2=[a2(x) a2(y) a2(z)]TIt is 2 three axis zero offset error of accelerometer;
a1(x) a1(y) a1(z) a1 is respectively represented in carrier system X, Y, the projection on Z axis;
a2(x) a2(y) a2(z) a is respectively represented2In carrier system X, Y, the projection on Z axis;
Z (k) is the error measurement vector at k moment;
ω and υ is respectively the process noise and measurement noise of corresponding dimension, is the white Gaussian noise of zero-mean, and meet
ω~N (0, Q), υ~N (0, R), wherein Q, R respectively represent the covariance matrix of corresponding noise;
AkFor 2 state-transition matrix of accelerometer 1 and accelerometer at k moment, and AkMeet
Wherein: 0m×nLine number is represented as m, columns is the null matrix of n;Im×nLine number is represented as m, columns is the unit square of n
Battle array;
Represent the calculation matrix at k moment:
Wherein:
Error observation vector in the acquisition error calibration model is:
According to what is be calculatedWithEstablish 2 error model of 1 error model of accelerometer and accelerometer;
1 error model of accelerometer is:
2 error model of accelerometer is:
The error measurement vector of error calibration model is obtained by 1 error model of accelerometer and 2 error model of accelerometer:
Use ObkCalculating is filtered as kalman filtering input.
The beneficial effects of the present invention are:
(1) scaling scheme designed by the present invention can be realized under conditions of no turntable to the accurate of accelerometer bias
Calibration, gets rid of the dependence in traditional scaling method for turntable, effectively extends scaling scheme
Application range and ease for use.
(2) in view of inertial navigation system commercial at present is equipped at least two accelerometer equipment, this programme can
Two sets of accelerometers are carried out Combined Treatment, can be completed at the same time by a calibration experiment to two sets of accelerometer equipment
On-line proving, ensured the agility and simplicity of scaling scheme.
(3) present invention devises a kind of dual acceleration meter error calibration model, and the model is merely with accelerometer information standard
The mathematical relationship between inertial navigation velocity error and accelerometer bias really is constructed, inertial navigation system speed is being obtained
On the basis of error, it can be realized by this models coupling kalman filtering technique and the accurate of accelerometer bias is estimated online
Meter.
The present invention will be described in detail with reference to the accompanying drawings and examples.
Detailed description of the invention
Fig. 1 is the dual acceleration meter calibration method flow diagram under the conditions of no turntable.
Specific embodiment
A kind of dual acceleration meter calibration method under the conditions of no turntable, is in carrier inertial navigation system to accelerometer
Carry out online error calibration, at least there are two accelerometer in carrier inertial navigation system, be referred to as accelerometer 1 and plus
Carrier inertial navigation system is placed in stationary state first by speedometer 2;Do not make
Under conditions of turntable, the calibration of accelerometer is realized.
The core concept of the scaling scheme is to require inertial navigation system generally in stationary state, utilizes accelerometer 1
Three axis output (is defined as: f1) pitch angle and roll angle of inertial navigation system under current state are calculated, while assuming to work as
The course angle of preceding inertial navigation system is 0 degree, then can obtain and be turned using the posture that accelerometer 1 provides information as reference input
Change matrix (is defined as: C1), pose transformation matrix is transition matrix of the carrier coordinate system to navigational coordinate system;Due to different seats
Calibration justice has the different derivations of equation, and therefore, the XYZ axis for defining carrier coordinate system corresponds respectively to the right front upper of carrier, fixed
The XYZ axis of adopted navigational coordinate system corresponds respectively to local northeast day, then, utilizes C1It is (fixed to the three axis output of accelerometer 2
Justice are as follows: f2) converted, and gravity compensation is carried out to result, obtain C1f2- g, wherein g is gravitational vectors under navigational coordinate system
Three axial projections, C can be obtained using same method2f1- g, in which: C2To provide information as with reference to defeated using accelerometer 2
The pose transformation matrix for entering and obtaining;If the output of accelerometer 1 and accelerometer 2 does not include any error, should expire
Sufficient C1f2- g=0, C2f1- g=0, but in practice due to the presence of various errors, C1f2- g and C2f1- g is not zero, can
To establish C1f2- g and C2f1The mathematical relationship of the zero bias of-g and acceleration 1 and accelerometer 2, so using the mathematical relationship with
C1f2- g and C2f1The value of-g completes the On-line Estimation to the zero bias of acceleration 1 and accelerometer 2, to realize accelerometer 1
With the error calibration of accelerometer 2.The maximum of the program is characterized in that ease for use, is providing the item of high-precision reference without turntable
Under part, the accurate Fast Calibration of accelerometer can be realized.
Since inertial navigation system is constantly in stationary state during the calibration process, i.e. three axle speeds of navigational coordinate system increase
Amount should be 0, i.e. C1f2- g and C2f1The theoretical value of-g is 0, then constructs error observed quantity and error observation model, building accordingly
Mathematical relationship between accelerometer 1 and the zero bias and three axle speed increments of accelerometer 2, and then correlation is filtered using kalman
The estimation of technology completion accelerometer bias.Algorithm
Overall flow figure is as shown in Figure 1.
Therefore, which comprises
1,2 zero offset error peg model of accelerometer 1 and accelerometer is constructed and defines, while obtaining error calibration model
In error measurement vector;
2, accelerometer 1 and 2 zero offset error peg model of accelerometer are filtered with kalman filtering method, it will accidentally
Poor observation vector as filtering input, miss by three axis of the k moment output zero bias that accelerometer 1 is obtained from the convergence process to filtering
Three axis of k moment of difference and accelerometer 2 exports zero offset error;
3, using three axis of k moment of accelerometer 1 and accelerometer 2 output zero offset error numerical value as calibration value, complete mark
It is fixed.
Wherein: described to construct and be the step of defining 2 zero offset error peg model of accelerometer 1 and accelerometer:
Step 1: being calculated by the three axis output of the accelerometer 1 and accelerometer 2 of acquisition stationary state moment k quiet
The only roll angle and pitch angle initial value of the roll angle of the accelerometer 1 of state and pitch angle initial value and accelerometer 2;
When the XYZ axis of carrier coordinate system corresponds respectively to the right front upper of carrier, the XYZ axis of navigational coordinate system is local east
When northern day:
Its calculation formula is respectively as follows:
Wherein:
It respectively representsIn carrier system X, Y, the projection on Z axis;
It respectively representsIn carrier system X, Y, the projection on Z axis;
WithIt is to be exported by 1 three axis of accelerometer respectivelyThe roll angle and pitching angle value being calculated;
WithIt is to be exported by 2 three axis of accelerometer respectivelyThe roll angle and pitching angle value being calculated;
Atan represents arctan function, and asin represents arcsin function;
G represents local gravitational acceleration;
In the middleIt is that original three axis of the accelerometer 1 at the k moment exports
(containing error);It is that original three axis output of the accelerometer 2 at the k moment (contains
Error);WithIt is to remain static to be derived by inertial navigation system;
Step 2: passing through the course angle true value for setting the k moment as ψk=0, it usesAnd ψkIt is defeated to construct accelerometer 1
Out carrier coordinate system to navigational coordinate system pose transformation matrixAnd it uses And ψkThe output of accelerometer 2 is constructed to carry
Body coordinate system to navigational coordinate system pose transformation matrix
Step 3: defining 2 zero offset error peg model of accelerometer 1 and accelerometer using pose transformation matrix:
X (k+1)=Akx(k)+ω
Z (k)=Hkx(k)+υ
Wherein:
It is the error state vector of accelerometer 1 and accelerometer 2 at the k moment,
a1=[a1(x) a1(y) a1(z)]TIt is 1 three axis zero offset error of accelerometer;
a2=[a2(x) a2(y) a2(z)]TIt is 2 three axis zero offset error of accelerometer;
a1(x) a1(y) a1(z) a is respectively represented1In carrier system X, Y, the projection on Z axis;
a2(x) a2(y) a2(z) a is respectively represented2In carrier system X, Y, the projection on Z axis;
Z (k) is the error measurement vector at k moment;
ω and υ is respectively the process noise and measurement noise of corresponding dimension, is the white Gaussian noise of zero-mean, and meet
ω~N (0, Q), υ~N (0, R), wherein Q, R respectively represent the covariance matrix of corresponding noise;
AkFor 2 state-transition matrix of accelerometer 1 and accelerometer at k moment, and AkMeet
Wherein: 0m×nLine number is represented as m, columns is the null matrix of n,;Im×nLine number is represented as m, columns is the unit square of n
Battle array, m and n can be respectively set as 3;
Represent the calculation matrix at k moment:
Wherein:
Error observation vector in the acquisition error calibration model is:
According to what is be calculatedWithEstablish 2 error model of 1 error model of accelerometer and accelerometer;
1 error model of accelerometer is:
2 error model of accelerometer is:
The error measurement vector of error calibration model is obtained by 1 error model of accelerometer and 2 error model of accelerometer:
Use ObkCalculating is filtered as kalman filtering input.
In dual acceleration meter error calibration model and error observation vector ObkOn the basis of, utilize kalman filtering method
It is filtered, by model:As filtering object, by ObkIt is filtered as kalman defeated
Enter to be filtered the estimated result that accelerometer bias is calculated, kalman filtering method is a kind of well-known technique, this implementation
Example no longer repeats it.
The estimation procedure of accelerometer bias is as follows:
Pk,k-1=APk-1AT+Q
Kk=Pk,k-1Hk T[HkPk,k-1Hk T+R]-1
Pk=[I6×6-KkHk]Pk,k-1
Wherein,K-1 moment filter result is represented,K moment filter result is represented,Represent the shape at k-1 moment
State one-step prediction, Pk,k-1Represent the prediction error variance at k-1 moment, KkRepresent the filtering gain at k moment, PkRepresenting the k moment filters
Wave error variance, Pk-1Represent the filtering error variance at k-1 moment, I6×6Representing line number is 6, the unit matrix that columns is 6.Its
In,For the estimated result of x (k), whereinWithIt respectively represents to a1With a2In kth
The estimated value at quarter.
It is finally obtained after waiting filter result convergence through filtering processing after a period of timeStable convergence value, definition
The stable convergence of filtering is realized in L step, then is extractedInWithComplete accelerometer 1
With the zero bias on-line proving of accelerometer 2.
In conclusion the above is merely preferred embodiments of the present invention, being not intended to limit the scope of the present invention.
All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in of the invention
Within protection scope.
Claims (2)
1. the dual acceleration meter calibration method under the conditions of a kind of no turntable, be in carrier inertial navigation system to accelerometer into
Row error calibration, at least there are two accelerometers in carrier inertial navigation system, are referred to as accelerometer 1 and accelerometer
2, carrier inertial navigation system is placed in stationary state first, which is characterized in that the described method includes:
2 zero offset error peg model of accelerometer 1 and accelerometer is constructed and defined, while obtaining the mistake in error calibration model
Difference measurements vector;
Accelerometer 1 and 2 zero offset error peg model of accelerometer are filtered with kalman filtering method, error is observed
Vector obtains three axis of the k moment output zero offset error of accelerometer 1 as filtering input from the convergence process to filtering, with
And three axis of k moment of accelerometer 2 exports zero offset error;
Using three axis of k moment of accelerometer 1 and accelerometer 2 output zero offset error numerical value as calibration value, calibration is completed.
2. scaling method according to claim 1, it is characterised in that:
It is described to construct and be the step of defining 2 zero offset error peg model of accelerometer 1 and accelerometer:
Step 1: static shape is calculated in the three axis output by the accelerometer 1 and accelerometer 2 of acquisition stationary state moment k
The roll angle and pitch angle initial value of the accelerometer 1 of state and the roll angle and pitch angle initial value of accelerometer 2;
When the XYZ axis of carrier coordinate system corresponds respectively to the right front upper of carrier, the XYZ axis of navigational coordinate system is local northeast day
When:
Its calculation formula is respectively as follows:
Wherein:
It respectively representsIn carrier system X, Y, the projection on Z axis;
It respectively representsIn carrier system X, Y, the projection on Z axis;
WithIt is to be exported by 1 three axis of accelerometer respectivelyThe roll angle and pitching angle value being calculated;
WithIt is to be exported by 2 three axis of accelerometer respectivelyThe roll angle and pitching angle value being calculated;
Atan represents arctan function, and asin represents arcsin function;
G represents local gravitational acceleration;
Step 2: passing through the course angle true value for setting the k moment as ψk=0, it usesAnd ψkIt constructs accelerometer 1 and exports carrier
Coordinate system to navigational coordinate system pose transformation matrixAnd it usesAnd ψkIt constructs accelerometer 2 and exports carrier seat
Mark is to the pose transformation matrix of navigational coordinate system
Step 3: defining 2 zero offset error peg model of accelerometer 1 and accelerometer using pose transformation matrix:
X (k+1)=Akx(k)+ω
Z (k)=Hkx(k)+υ
Wherein:
It is the error state vector of accelerometer 1 and accelerometer 2 at the k moment,
a1=[a1(x) a1(y) a1(z)]TIt is 1 three axis zero offset error of accelerometer;
a2=[a2(x) a2(y) a2(z)]TIt is 2 three axis zero offset error of accelerometer;
a1(x) a1(y) a1(z) a is respectively represented1In carrier system X, Y, the projection on Z axis;
a2(x) a2(y) a2(z) a is respectively represented2In carrier system X, Y, the projection on Z axis;
Z (k) is the error measurement vector at k moment;
ω and υ is respectively the process noise and measurement noise of corresponding dimension, is the white Gaussian noise of zero-mean, and meet ω~
N (0, Q), υ~N (0, R), wherein Q, R respectively represent the covariance matrix of corresponding noise;
AkFor 2 state-transition matrix of accelerometer 1 and accelerometer at k moment, and AkMeet
Wherein: 0m×nLine number is represented as m, columns is the null matrix of n;Im×nLine number is represented as m, columns is the unit matrix of n;
Represent the calculation matrix at k moment:
Wherein:
Error observation vector in the acquisition error calibration model is:
According to what is be calculatedWithEstablish 2 error model of 1 error model of accelerometer and accelerometer;
1 error model of accelerometer is:
2 error model of accelerometer is:
The error measurement vector of error calibration model is obtained by 1 error model of accelerometer and 2 error model of accelerometer:
Use ObkCalculating is filtered as kalman filtering input.
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CN112325846A (en) * | 2020-10-21 | 2021-02-05 | 北京航空航天大学 | RTK tilt measurement precision improving method |
CN114324979A (en) * | 2022-01-06 | 2022-04-12 | 北京轩宇空间科技有限公司 | Accelerometer vibration detuning error evaluation method and device, storage medium and equipment |
CN114324979B (en) * | 2022-01-06 | 2024-04-02 | 北京轩宇空间科技有限公司 | Accelerometer vibration imbalance error assessment method, accelerometer vibration imbalance error assessment device, storage medium and accelerometer vibration imbalance error assessment device |
CN115655270A (en) * | 2022-11-30 | 2023-01-31 | 湖南航天机电设备与特种材料研究所 | Inertial measurement unit equivalent zero offset error compensation method and system |
CN115655270B (en) * | 2022-11-30 | 2024-04-19 | 湖南航天机电设备与特种材料研究所 | Inertial measurement unit equivalent zero offset error compensation method and system |
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