CN109084756A - A kind of gravity apparent motion parameter identification and accelerometer bias separation method - Google Patents

A kind of gravity apparent motion parameter identification and accelerometer bias separation method Download PDF

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CN109084756A
CN109084756A CN201810635511.9A CN201810635511A CN109084756A CN 109084756 A CN109084756 A CN 109084756A CN 201810635511 A CN201810635511 A CN 201810635511A CN 109084756 A CN109084756 A CN 109084756A
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apparent motion
formula
gravity apparent
accelerometer
gravity
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CN109084756B (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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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Manufacturing & Machinery (AREA)
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Abstract

The present invention discloses a kind of gravity apparent motion parameter identification and accelerometer bias separation method, comprising the following steps: building constructs gravity apparent motion/accelerometer bias coupling model based on gravity apparent motion；Construct accelerometer bias separation and identification model；Utilize the observed quantity of acquisitionThe state vector of selecting system；Gravity apparent motion parameter identification is carried out by Kalman filter to separate with accelerometer bias.Using gravity apparent motion parameter identification provided by the present application and accelerometer bias separation method, under the conditions of zero-speed, swaying base, gravity apparent motion parameter identification is carried out to separate with accelerometer bias, parsing alignment is carried out using the gravity apparent motion after reconstruct, carrier levels attitude error approaches zero.

Description

A kind of gravity apparent motion parameter identification and accelerometer bias separation method
Technical field
The present invention relates to a kind of gravity apparent motion parameter identifications and accelerometer bias separation method, belong to navigation algorithm Technical field.
Background technique
Inertial navigation system is a kind of navigation system based on integral working method, and instrument error is during integral It is accumulated, so system position error rapid growth over time.It is generally acknowledged that instrument error, especially gyroscope, accelerates Degree meter constant value zero bias are the key factors of decision systems precision.Therefore it often carries out including instrument error before system navigation work Initial alignment including estimation.
System working site does not have external high precision turntable equipment generally, is often relied on system-level calibration.System-level mark School needs to refer to external high-precision navigation information, and wherein speed is a kind of most common, external reference information for most easily obtaining, such as The GNSS auxiliary speed etc. in zero velocity constraint, GNSS/SINS combination in zero-velocity curve.Accelerometer bias integral is shown as Velocity error can obtain accelerometer bias according to velocity error with inverting.But in the system-level calibration based on speeds match Cheng Zhong exists between accelerometer bias and the horizontal misalignment of INS and couples, east orientation gyro error, north orientation accelerometer bias Exist between INS azimuthal misalignment angle and couples.It decouples above-mentioned error and extra demand is proposed to the maneuverability of carrier.Such as warship Ship, carrier vehicle, large-scale flight etc. can not carry out the somersault of fighter plane class, high maneuver movement.Carrier maneuverability is not being proposed Under the premise of extra demand, completes accelerometer bias calibration and still have difficulty.
In addition, if carrier exist shake or (and) navigation system/carrier system be not overlapped, accelerate due to that can not determine in carrier system Projection of the degree meter zero bias in navigation system directly can not carry out calibration to accelerometer using the method compared, need separately to ward off footpath Diameter.
Summary of the invention
Goal of the invention: it is an object of the invention to not to carrier maneuverability propose extra demand under the premise of, only Using the constraint of carrier zero-speed and itself excitation of the shaking to error, such as ship sway moves under wind and wave exciting, finds one Class accelerometer bias Calibration Method.
Technical solution: the present invention the following technical schemes are provided:
A kind of gravity apparent motion parameter identification and accelerometer bias separation method, comprising the following steps:
1) it establishes based on gravity apparent motion building gravity apparent motion and accelerometer bias coupling model；
2) separation of building accelerometer bias and identification model；
3) observed quantity obtained is utilizedThe state vector of selecting system；
4) gravity apparent motion parameter identification is carried out by Kalman filter to separate with accelerometer bias.
Further, step 1) described in feature is based on gravity apparent motion and constructs gravity apparent motion/accelerometer bias Coupling model specifically comprises the following steps:
In the case where carrier does not have line movement, the theoretical vector that accelerometer measures is exactly gravitational vectors in carrier system b Projection under system, it is as follows to provide gravity apparent motion expression-form using projection of the acceleration measuring magnitude under inertial system:
In formula, i is inertial coodinate system, in0Navigational coordinate system, e for initial time0For initial time terrestrial coordinate system, E be current time terrestrial coordinate system,Indicate the pose transformation matrix from B to A；In above-mentioned each attitude matrix,With It is constant value matrix；When carrier radio motionIt also is constant value；It is related to time, rotational-angular velocity of the earth for one Matrix；
It will determine that value constant substitutes and be unfolded above formula, have:
In formula, a11~a33、b11~b33、c11~c33With A11~A33It is constant value；ωieIt is respectively earth rotation angle speed with g The value of degree and acceleration of gravity；T is observing time length；
When selecting initial time carrier coordinate system as inertial system, can define inertial system i is ib0, gravity apparent motion can It is calculated according to accelerometer and gyroscope instrument measured value, specific formula for calculation is as follows:
In formula (3),For gravity apparent motion calculated value,For current time carrier system and initial time carrier system Between attitude matrix,For acceleration measuring magnitude；WhereinIt can integrate to obtain by gyro, calculation formula is as follows:
Consider that accelerometer constant value zero bias and random noise, accelerometer measures model can be expressed as follows:
In formula, ▽bWith ηbAccelerometer constant value zero bias and random noise respectively；It brings formula (5) into formula (3), and ignores gyro Instrument measurement error, has:
Further, the separation of the step 2) building accelerometer bias and identification model, specifically include:
Gravity apparent motion true valueThe gravity apparent motion value substitution after reconstruct can be used, i.e., brought formula (2) into Formula (6), has:
C in formula11~33For matrixCorresponding element；For ▽bEach axis component under b system of carrier system；ForIn ib0It is each axis component, is random noise；Formula (9) formally separates gravity apparent motion with accelerometer bias It comes, if can estimate to obtain A by certain form11~A33WithGravity apparent motion parameter identification and acceleration then can be achieved The decoupling of zero bias.
Further, the step 3) utilizes the observed quantity obtainedThe state vector of selecting system is specific to wrap It includes:
Utilize the observed quantity of acquisitionEstimate optimal parameter；Take A11~A33WithFor state vector, i.e.,
Analysis is it is found that when inertial system has determined above, A11~A33For fixed value.
Further, the step 4) carries out gravity apparent motion parameter identification and accelerometer zero by Kalman filter Separation partially specifically:
A11~A33For fixed value, then visual above-mentioned amount is constant value in a short time, to there is system state equation are as follows:
Xk=Xk-1 \*MERGEFORMAT(9)
Taking gravity apparent motion is measuring value, i.e.,
According to formula (7), there is measurement matrix are as follows:
C in formula11~33It is matrixIn element, formula (11)~(14) constitute system state equation and measure Equation.Based on above-mentioned equation, above-mentioned quantity of state can be carried out using the least square method of recursion based on Kalman filter form Estimation；On-line identification filter based on recursive least-squares can construct as follows:
In formula, k indicates calculation times, and K indicates filtering gain, and P indicates that error covariance, R indicate error in measurement, and I is indicated Unit matrix.
Compared with prior art, the present invention the beneficial effect is that: with gravity apparent motion parameter identification provided by the present application with Accelerometer bias separation method carries out gravity apparent motion parameter identification and accelerometer zero under the conditions of zero-speed, swaying base Separation partially, carries out parsing alignment using the gravity apparent motion after reconstruct, carrier levels attitude error approaches zero, specific table It is existing are as follows:
1) in initial alignment process, extra demand is not proposed to carrier maneuverability；
2) in alignment procedures, the external drives such as carrier is constrained merely with zero-speed and itself shakes；
3) recursive algorithm is combined with least square method, with based on Kalman filter form least square method of recursion into The estimation of the above-mentioned quantity of state of row；
4) in alignment procedures, accelerometer constant value zero bias can be demarcated, the navigation calculation or other equipment for SINS use.
Detailed description of the invention
Fig. 1 is the gravity apparent motion schematic diagram that the present invention uses；
Fig. 2 is accelerometer bias estimated result figure under the conditions of swaying base of the present invention；
Alignment result figure under the conditions of Fig. 3 swaying base of the present invention.
Specific embodiment
Technical solution of the present invention is described in detail below, but protection scope of the present invention is not limited to the implementation Example.
Embodiment
The present invention is based on gravity apparent motions in inertial system, construct gravity apparent motion/accelerometer bias coupling model, then Accelerometer bias separation and identification model are constructed, the observed quantity of acquisition is utilizedThe state vector of selecting system, Gravity apparent motion parameter identification is carried out by Kalman filter to separate with accelerometer bias.
Implementation method of the present invention is described in more detail with reference to the accompanying drawing:
Fig. 1 is the gravity apparent motion schematic diagram that the present invention uses, and the weight of certain point with earth rotation is observed in inertial system Power acceleration is directed toward the variation with size, constitutes the circular cone.
Specifically comprised the following steps: based on gravity apparent motion building gravity apparent motion/accelerometer bias coupling model
In the case where carrier does not have line movement, the theoretical vector that accelerometer measures is exactly gravitational vectors in carrier system b Projection under system, it is as follows to provide gravity apparent motion expression-form using projection of the acceleration measuring magnitude under inertial system:
In formula, i is inertial coodinate system, in0Navigational coordinate system, e for initial time0For initial time terrestrial coordinate system, E be current time terrestrial coordinate system,Indicate the pose transformation matrix from B to A.In above-mentioned each attitude matrix,With It is constant value matrix；When carrier radio motionIt also is constant value；It is related to time, rotational-angular velocity of the earth for one Matrix.It will determine that value constant substitutes and be unfolded above formula, have:
In formula, a11~a33、b11~b33、c11~c33With A11~A33It is constant value；ωieIt is respectively earth rotation angle speed with g The value of degree and acceleration of gravity；T is observing time length.
When selecting initial time carrier coordinate system as inertial system, can define inertial system i is ib0, gravity apparent motion can It is calculated according to accelerometer and gyroscope instrument measured value, specific formula for calculation is as follows:
In formula (3),For gravity apparent motion calculated value,For current time carrier system and initial time carrier system Between attitude matrix,For acceleration measuring magnitude.WhereinIt can integrate to obtain by gyro, calculation formula is as follows:
Consider that accelerometer constant value zero bias and random noise, accelerometer measures model can be expressed as follows:
In formula, ▽bWith ηbAccelerometer constant value zero bias and random noise respectively.It brings formula (5) into formula (3), and ignores gyro Instrument measurement error, has:
Accelerometer bias separation and identification model are constructed, is specifically included:
Gravity apparent motion true valueThe gravity apparent motion value substitution after reconstruct can be used, i.e., brought formula (2) into Formula (6), has:
\*MERGEFORMAT(7)
C in formula11~33For matrixCorresponding element；For ▽bEach axis component under b system of carrier system；ForIn ib0It is each axis component, is random noise.Formula (9) formally separates gravity apparent motion with accelerometer bias It comes, if can estimate to obtain A by certain form11~A33WithGravity apparent motion parameter identification and acceleration then can be achieved The decoupling of zero bias.
Utilize the observed quantity of acquisitionThe state vector of selecting system, specifically includes:
Utilize the observed quantity of acquisitionEstimate optimal parameter.Take A11~A33WithFor state vector, i.e.,
When inertial system has determined, A11~A33For fixed value,.
Gravity apparent motion parameter identification is carried out by Kalman filter to separate with accelerometer bias specifically:
A11~A33For fixed value, then visual above-mentioned amount is constant value in a short time, to there is system state equation are as follows:
Xk=Xk-1 \*MERGEFORMAT(9)
Taking gravity apparent motion is measuring value, i.e.,
According to formula (7), there is measurement matrix are as follows:
C in formula11~33It is matrixIn element, formula (11)~(14) constitute system state equation and measurement side Journey.It, can be using the estimation for carrying out above-mentioned quantity of state based on Kalman filter form least square method of recursion based on above-mentioned equation. It can be constructed based on the on-line identification filter based on Kalman filter form recursive least-squares as follows:
In formula, k indicates calculation times, and K indicates filtering gain, and P indicates that error covariance, R indicate error in measurement, and I is indicated Unit matrix.
Beneficial effects of the present invention are verified by following emulation experiment:
The setting of Matlab simulated conditions
Naval vessel is in zero-speed vibrating state, and vessel roll gym suit is from Asin (2 π ft+ β0)+θ0, wherein A is to shake Amplitude, f are the frequency shaken, β0It is starting phase angle, θ0It is the initial attitude angle of naval vessel Relative Navigation coordinate system.Relevant parameter Setting is as shown in the table.The initial longitude and latitude in naval vessel is respectively 118 ° and 32 ° of north latitude of east longitude.
Table 1 waves parameter setting
Pitching Rolling Course
Wave amplitude (°) 6 13 8
Rolling period (s) 10 8 8
Initial phase (°) 0 0 0
Initial angle (°) 2 6 5
Accelerometer and gyroscope ideal data are generated using reverse navigation algorithm according to the above-mentioned characteristics of motion.In ideal Instrumented data on add instrument constant error and random error, generate have error instrumented data, for simulating practical instrument The data of table output, the frequency that instrumented data generates is 100Hz.The setting of the error parameter of accelerometer and gyro is shown in Table 2. wherein Random noise meets white noise hypothesis.
The setting of 2 instrument error of table
Alignment and the verifying for adding the estimation of table zero bias
Proof of algorithm is carried out in ordinary PC.It emulates and carries out 4000s, during simulation process, (1) generates instrumented data； (2) gravity apparent motion is calculated using gyroscope and acceleration measuring magnitude；(3) gravity apparent motion ginseng is carried out by Kalman filter Number identification accelerometer bias separation；(4) parsing alignment is carried out using the gravity apparent motion after reconstruct；(5) it repeats the above steps. Fig. 2 and 3 is respectively accelerometer constant value zero offset error and alignment result.
Fig. 2 illustrates the accelerometer constant value zero bias estimated value under the conditions of shaking, radio motion pedestal, and wherein solid line indicates Error estimate, dotted line indicate error true value.Curve shows that three axis accelerometer zero bias are equal under the conditions of shaking, radio motion Can largely it be estimated, estimated result and true value error are smaller；
Fig. 3, which is illustrated, to be reconstructed gravity apparent motion using gravity apparent motion identified parameters and parses pair of alignment methods acquisition Standard is as a result, wherein dotted line indicates pair of the strapdown compass Initial Alignment Method (method 1) based on inertial system gravity apparent motion Quasi- result], solid line indicates the alignment result (method 2) after separate accelerometer zero bias, ideal eP is drawn simultaneously in figure, Ideal eR, ideal eH divides table to indicate pitch angle, roll angle and course angle theory alignment precision value, and draws zero curve zero. Curve shows gravity apparent motion calculated value after separate accelerometer constant value zero bias, and horizontal aligument precision is greatly improved, and level is lost Quasi- angle error programmable single-chip system is in zero.
As described above, must not be explained although the present invention has been indicated and described referring to specific preferred embodiment For the limitation to invention itself.It without prejudice to the spirit and scope of the invention as defined in the appended claims, can be right Various changes can be made in the form and details for it.

Claims (5)

1. a kind of gravity apparent motion parameter identification and accelerometer bias separation method, which comprises the following steps:
1) it establishes based on gravity apparent motion building gravity apparent motion and accelerometer bias coupling model；
2) separation of building accelerometer bias and identification model；
3) observed quantity obtained is utilizedThe state vector of selecting system；
4) gravity apparent motion parameter identification is carried out by Kalman filter to separate with accelerometer bias.
2. a kind of gravity apparent motion parameter identification according to claim 1 and accelerometer bias separation method, feature The step 1) is based on gravity apparent motion building gravity apparent motion/accelerometer bias coupling model and specifically includes following step It is rapid:
In the case where carrier does not have line movement, the theoretical vector that accelerometer measures is exactly gravitational vectors under b system of carrier system Projection, it is as follows to provide gravity apparent motion expression-form using projection of the acceleration measuring magnitude under inertial system:
In formula, i is inertial coodinate system, in0Navigational coordinate system, e for initial time0It is for terrestrial coordinate system, the e of initial time The terrestrial coordinate system at current time,Indicate the pose transformation matrix from B to A；In above-mentioned each attitude matrix,With? For constant value matrix；When carrier radio motionIt also is constant value；It is relevant to time, rotational-angular velocity of the earth for one Matrix；
It will determine that value constant substitutes and be unfolded above formula, have:
In formula, a11~a33、b11~b33、c11~c33With A11~A33It is constant value；ωieWith g be respectively rotational-angular velocity of the earth with The value of acceleration of gravity；T is observing time length；
When selecting initial time carrier coordinate system as inertial system, can define inertial system i is ib0, gravity apparent motion can basis Accelerometer is calculated with gyroscope instrument measured value, and specific formula for calculation is as follows:
In formula (3),For gravity apparent motion calculated value,The appearance between current time carrier system and initial time carrier system State matrix,For acceleration measuring magnitude；WhereinIt can integrate to obtain by gyro, calculation formula is as follows:
Consider that accelerometer constant value zero bias and random noise, accelerometer measures model can be expressed as follows:
In formula, ▽bWith ηbAccelerometer constant value zero bias and random noise respectively；It brings formula (5) into formula (3), and ignores gyroscope survey Error is measured, is had:
3. a kind of gravity apparent motion parameter identification according to claim 1 and accelerometer bias separation method, feature It is, step 2) the building accelerometer bias separation and identification model specifically include:
Gravity apparent motion true valueThe gravity apparent motion value substitution after reconstruct can be used, i.e., bring formula (2) into formula (6), have:
C in formula11~33For matrixCorresponding element；For ▽bEach axis component under b system of carrier system；For In ib0It is each axis component, is random noise；Formula (9) formally separates gravity apparent motion with accelerometer bias, if It can estimate to obtain A by certain form11~A33WithThe solution of gravity apparent motion parameter identification and acceleration zero bias then can be achieved Coupling.
4. a kind of gravity apparent motion parameter identification according to claim 1 and accelerometer bias separation method, feature It is, the step 3) utilizes the observed quantity obtainedThe state vector of selecting system, specifically includes:
Utilize the observed quantity of acquisitionEstimate optimal parameter；Take A11~A33WithFor state vector, i.e.,
Analysis is it is found that when inertial system has determined above, A11~A33For fixed value.
5. a kind of gravity apparent motion parameter identification according to claim 1 and accelerometer bias separation method, feature It is, the step 4) carries out gravity apparent motion parameter identification by Kalman filter and separates specifically with accelerometer bias Are as follows:
A11~A33For fixed value, then visual above-mentioned amount is constant value in a short time, to there is system state equation are as follows:
Xk=Xk-1 \*MERGEFORMAT(9)
Taking gravity apparent motion is measuring value, i.e.,
According to formula (7), there is measurement matrix are as follows:
C in formula11~33It is matrixIn element, formula (11)~(14) constitute system state equation and measurement equation. It, can be using the estimation for carrying out above-mentioned quantity of state based on the least square method of recursion of Kalman filter form based on above-mentioned equation； On-line identification filter based on recursive least-squares can construct as follows:
In formula, k indicates calculation times, and K indicates filtering gain, and P indicates that error covariance, R indicate error in measurement, and I indicates unit Matrix.
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