CN108225312A - A kind of GNSS/INS pine combinations Caused by Lever Arm estimation and compensation method - Google Patents
A kind of GNSS/INS pine combinations Caused by Lever Arm estimation and compensation method Download PDFInfo
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- CN108225312A CN108225312A CN201711438761.5A CN201711438761A CN108225312A CN 108225312 A CN108225312 A CN 108225312A CN 201711438761 A CN201711438761 A CN 201711438761A CN 108225312 A CN108225312 A CN 108225312A
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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
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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
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/48—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system
- G01S19/49—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system whereby the further system is an inertial position system, e.g. loosely-coupled
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Abstract
The invention discloses a kind of estimations of GNSS/INS pine combinations Caused by Lever Arm and compensation method, problem to be solved by this invention to be：It is inconvenient to be measured for GNSS/INS pine combination navigation system Caused by Lever Arm Effect, and navigation procedure Caused by Lever Arm Effect constantly variation so as to influence integrated navigation system navigation accuracy the problem of, it is proposed a kind of method for estimating lever arm as Kalman filtering quantity of state, this method need not be determined in advance inertial navigation and defend the lever arm between lead antenna, so as to avoid before navigation to the measurement process of lever arm, it in addition to this can be in effective compensation navigation procedure, caused by being shaken due to carrier the problem of lever arm error real-time change.
Description
Technical field
The present invention relates to pass through karr in GNSS/INS integrated navigation fields more particularly to GNSS/INS integrated navigation systems
Graceful filtering algorithm solve between GNSS antenna and INS due to installation site it is misaligned caused by lever arm effect estimation and compensation
Method.
Background technology
When observation condition is good, GNSS device works independently with regard to that can obtain reliable navigation results.However in high building woods
Under the severe observation condition such as vertical city, forest, valley, when visible satellite quantity is less than four, GNSS can not be led
Boat resolves.INS has higher information renewal frequency, after the completion of initialization, the angular speed and specific force that are measured by itself
Information can calculate the information such as position, speed, the posture of carrier, be influenced however, as by the accumulation of error, cause navigation fixed
Position calculation accuracy dissipates at any time.GNSS and INS has good complementarity, and combination of the two is capable of providing compared to single
System is more accurate, reliable navigator fix result.In GNSS/INS integrated navigations, GNSS provides the update letter that inertial navigation needs
Breath, so as to inhibit the diverging of inertial navigation information, and inertial navigation can export the navigator fix information of high sampling rate, as GNSS because of signal
When being blocked or interfering and interrupt, inertial navigation remains to work on to increase the reliability and robustness of system.
In practical navigation application, in order to which inertial navigation is enable accurately to reflect the posture of carrier, inertial navigation would generally be pacified
Dress is fixed on carrier inside, and good observation signal in order to obtain, receiver antenna are typically installed at carrier top.Due to
Inertial navigation and to defend lead antenna installation site inconsistent so as to produce lever arm effect.In order to obtain high-precision integrated navigation as a result,
It must carry out the compensation of lever arm effect.Traditional lever arm compensating method is to measure inertial navigation and receiver antenna before navigation carries out
Between lever arm, compensated during real-time navigation, however inertial navigation equipment and receiver antenna in practical applications
Installation is complicated so as to make troubles to measurement, the lever arm inaccuracy for measuring and obtaining is even resulted in, so as in Kalman Filter Estimation
In be difficult to accurately compensate for lever arm error, in addition to this for some Attitudes, in the application due to the presence of vibrations, lever arm
Not constant value but in real-time change state, therefore by lever arm error regard as a fixed constant value can give navigation estimation
Introduce error.Therefore it is the committed step for improving navigation accuracy that effective compensation is carried out to lever arm effect.
Invention content
Problem to be solved by this invention is：It is inconvenient to be measured for GNSS/INS pine combination navigation system Caused by Lever Arm Effect,
And navigation procedure Caused by Lever Arm Effect constantly variation so as to influence integrated navigation system navigation accuracy the problem of, propose it is a kind of will
The method that lever arm is estimated as Kalman filtering quantity of state, this method need not be determined in advance inertial navigation and defend between lead antenna
Lever arm, so as to avoid before navigation to the measurement process of lever arm, in addition to this can be in effective compensation navigation procedure due to carrying
Caused by body vibrations the problem of lever arm error real-time change.
Present disclosure is as follows：
A kind of GNSS/INS pine combinations Caused by Lever Arm estimation and compensation method, include the following steps：
Step 1：Establish the Kalman filter model for including lever arm effect；
Step 2：The noise matrix of Kalman filtering of the setting comprising lever arm effect, the noise of the Kalman filtering
Matrix includes Q gusts of the quantity of state noise matrix of reflection inertial navigation noise level, P gusts of state vector variance matrix and measurement noise
R gusts of matrix；
Step 3：The noise matrix of Kalman filtering using Kalman filter model and comprising lever arm effect is included
The Kalman prediction of lever arm effect and update obtain including the state vector of lever arm effect error；
Step 4：Lever arm effect is compensated using the state vector comprising lever arm effect error.
Wherein, step 1 specifically includes following steps：
1.1 choose the state vector of the Kalman filtering comprising lever arm effect, institute according to navigation system and navigation scenarios
Lever arm effect L=[the l statedx ly lz], the state vector of the Kalman filtering comprising lever arm effect is：
Wherein L is vectorial for lever arm effect, x0To include the state vector of position, speed, posture and ins error, x is
State vector comprising lever arm effect, lx、ly、lzFor lever arm under carrier coordinate system x, y, the residual error in z directions；
1.2 establish the state transition equation for the Kalman filtering for including lever arm effect：
xk=Φk,k-1xk-1+Γk-1Wk-1
In formula, xk,xk-1The respectively state vector at k and k-1 moment, Φk,k-1Be it is discrete after state-transition matrix,
Γk-1Battle array, W are driven for system noisek-1For the noise vector of state, Φk,k-1It is expressed as：
In above formula, F0The corresponding state-transition matrix of Kalman filter equation not include lever arm effect, I matrixes are single
Bit matrix；
1.3 establish the measurement equation for the Kalman filtering for including lever arm effect
Z=Hx+V
In formula, Z matrixes are the measurement information matrix of Kalman filtering, and V is to measure noise item, noise variance matrix R
Matrix representation, H-matrix are measurement equation coefficient matrix, and wherein H-matrix form is as follows：
In above formula, H0The corresponding measurement equation coefficient matrix of Kalman filtering not include lever arm effect, in formulaWherein M represents meridian circle radius, and N represents prime vertical radius, and h represents the earth of carrier
Height,For the direction cosine matrix from body coordinate system to navigational coordinate system, l is the lever arm effect under body coordinate system, and m, n divide
It Wei not matrix line number and columns not comprising the Kalman filter model of lever arm effect.
Wherein, the state vector in step 2 initially P gust of uncertain matrix and reflects the quantity of state of inertial navigation noise level
The setting method that Q gusts of noise matrix is as follows：
Q gusts of settings of quantity of state noise matrix of Kalman filtering are as follows：
Wherein Q0The corresponding noise battle array of Kalman filtering not include lever arm effect, QlIt is expressed as：
Wherein σlx、σly、σlzFor the error amount of lever arm effect, value 0.05；
Initially the P gusts of settings of uncertain matrix are as follows for the state vector of Kalman filtering：
Wherein, P0The corresponding state vector initial value of Kalman filtering not include lever arm effect is uncertain, PlIt represents
For：
Wherein, σlx0、σly0、σlz0The uncertainty of lever arm effect initial value is represented, when lever arm effect initial value is set as zero
When, which is selected according to application scenarios.
Wherein, step 3 is specially：
The prediction process of Kalman filtering：
xk+1=Φkxk
Wherein, ΦkFor state-transition matrix, xk、xk+1The state vector at k moment and k+1 moment, Q are represented successivelykIt represents
The quantity of state noise matrix at k moment, Pk、Pk+1The state vector variance matrix at k moment and k+1 moment is represented successively；
The renewal process of Kalman filtering：
xk+1=xk+Kk(Zk-Hkxk)
Pk+1=(I-KkHk)Pk
Wherein KkRepresent the gain matrix at k moment, HkRepresent the measurement equation coefficient matrix at k moment, RkIt represents and measures noise
Matrix, I represent unit matrix, and Z is the measurement information matrix at k moment；
Prediction and update are completed to have obtained including the state vector of lever arm effect error.
Wherein, step 4 is specially：
Lever arm effect is compensated using the state vector comprising lever arm effect error, obtains lever arm effect：
lxk=lxk-1+lx
lyk=lyk-1+ly
lzk=lzk-1+lz
In formula, lxk、lyk、lzkBe followed successively by lever arm effect that k moment Kalman Filter Estimations obtain carrier coordinate system x,
Y, the component in z-axis direction, lxk-1、lyk-1、lzk-1Lever arm effect that k-1 moment Kalman Filter Estimations obtain is followed successively by carrier
The component of coordinate system x, y, z axis direction, lx,ly,lzIt is followed successively by residual on lever arm effect x, y, the z directions of Kalman Filter Estimation
Remaining error；By the corresponding Kalman filtering of lever arm effect if being compensated in Kalman filtering process lever arm effect
State vector corresponding entry zero setting, otherwise not zero setting.
Above step just completes the renewal process of a Kalman filtering, in entire navigation procedure, constantly carries out
The cycle calculations of Kalman filtering determine appearance information so as to provide continuous reliably navigation in entire navigation procedure.
Advantages of the present invention is：
Patent of the present invention is estimated lever arm effect value as the state vector of Kalman filtering, so as to avoid in reality
When navigation before lever arm is worth measuring, effectively increase navigation efficiency, while can avoid during carrier movement due to shaking
Presence and lever arm value is caused constantly to change the navigation error of introducing.
Description of the drawings
Fig. 1 is Kalman filtering structures block diagram.
Fig. 2 lever arm effect schematic diagrames.
Specific embodiment
With reference to specific embodiments and the drawings, the present invention will be further described：
As shown in Figure 1, patent of the present invention mainly includes four steps, specific as follows：
Step 1：Establish the Kalman filter model for including lever arm effect.Sub-step is as follows：
1.1 choose the state vector of Kalman filtering according to the scene of navigation application, it is however generally that the quantity of state of selection is got over
It is more more accurately to reflect motion model, more accurately quantity of state can be estimated, in addition to this selection of quantity of state
Depending on used inertial navigation grade, such as the MEMS inertial navigations for inferior grade, scale factor and quadrature axis coupling error are larger,
It needs to consider when choosing quantity of state, can also increase therewith however as the complexity for increasing calculating of quantity of state, therefore
Considered when choosing quantity of state, in the present embodiment chosen position error, velocity error, attitude error, top
Spiral shell zero offset error, accelerometer bias error and lever arm error have 18 errors altogether as quantity of state.Quantity of state is as follows：
Wherein δ rN δrE δrDRepresent east northeast place to site error, δ vN δvE δvDRepresent east northeast place to speed
Error, ψN ψE ψDRepresent roll, pitching, course angle error, bgx bgy bgzRepresent gyro x, y, the zero offset error of z-axis, bax
bay bazRepresent accelerometer x, y, the zero offset error of z-axis, Δ lx Δ ly Δs lz represents lever arm effect in carrier coordinate system
Error on x, y, z direction.
1.2 establish the state transition equation for the Kalman filtering for including lever arm effect：
xk=Φk,k-1xk-1+Γk-1Wk-1
In formula, xk,xk-1The respectively state vector at k and k-1 moment, Φk,k-1Be it is discrete after state-transition matrix,
Γk-1Battle array, W are driven for system noisek-1For the noise vector of state, Φk,k-1It is expressed as：
Site error, velocity error, attitude error, gyro zero offset error, accelerometer bias are had chosen in the present embodiment
Error and lever arm error have 18 quantity of states its corresponding state-transition matrixes altogether：
Wherein：
Wherein, vE、vN、vDCarrier east orientation speed, north orientation speed and sky orientation speed, ω are represented successivelyeRepresent oneself of the earth
Angular speed, M, N are passed, h represents the geodetic height of earth prime vertical radius, meridian circle radius and carrier successively,Represent carrier latitude
Degree, γ represent local normal gravity, Δ t, TabRepresent sampling interval and the correlation time of inertial navigation noise.fb,fnIt represents and passes
Sensor exports the projection in carrier coordinate system and navigational coordinate system.
1.3 establish the measurement equation for the Kalman filtering for including lever arm effect
Zk=Hkxk+Vk
The measurement information matrix of Z matrix representatives Kalman filtering in above formula, V matrix representatives measure noise item, and H-matrix represents
Measurement equation coefficient matrix, wherein H-matrix form are as follows：
Wherein l represents lever arm value,The direction cosine matrix from carrier coordinate system to navigational coordinate system is represented,To carry
Body moves the projection in carrier coordinate system relative to inertial system,It is being led for navigational coordinate system relative to terrestrial coordinate system movement
The projection of boat coordinate system,The projection of navigational coordinate system is tied up to relative to inertial coordinate for terrestrial coordinate system.
The variance matrix R matrix representations for measuring noise item are as follows：
WhereinFor GNSS observation information east orientation position variances value, north orientation position side
Difference, day are to position variance value, east orientation speed variance yields, north orientation speed variance yields and sky orientation speed variance yields.
Step 2：Set the noise matrix of Kalman filtering.Kalman filtering noise matrix includes renewal equation noise Q
Battle array, P gusts of original state amount uncertainty matrix and R gusts of noise matrix of measurement.
The Q battle arrays setting of 2.1 Kalman filterings is as follows：
Qk=diag { 000 vrw2 vrw2 vrw2 arw2 arw2 arw2 Qgb Qgb Qgb Qab Qab Qab σlx σly
σlz}
Vrw represents the speed random walk of inertial sensor, arw represents the angle random walk of inertial sensor, Qgb,
QabThe output noise of inertial sensor is represented successively.
The measurement noise matrix of 2.2 Kalman filterings is as follows：
The P battle array initial values of 2.3 Kalman filterings reflect the initial uncertainty of state vector, the initial value P of P matrixes0If
It is fixed as follows：
Step 3：Kalman prediction and renewal process.
The prediction process of Kalman filtering：
xk+1=Φkxk
Wherein, ΦkFor state-transition matrix, xk、xk+1The state vector at k moment and k+1 moment, Q are represented successivelykIt represents
The quantity of state noise matrix at k moment, Pk、Pk+1The state vector variance matrix at k moment and k+1 moment is represented successively.
The renewal process of Kalman filtering：
xk+1=xk+Kk(Zk-Hkxk)
Pk+1=(I-KkHk)Pk
Wherein KkRepresent the gain matrix at k moment, HkRepresent the measurement equation coefficient matrix at k moment, RkRepresent the k moment
Noise matrix is measured, I represents unit matrix.
Step 4：Compensation Feedback.
Just estimation has obtained including the state vector of lever arm effect error after Kalman filtering update, can obtain at this time
Lever arm effect：
lxk=lxk-1+lx
lyk=lyk-1+ly
lzk=lzk-1+lz
The lx in above formulak、lyk、lzkLever arm effect that k epoch Kalman Filter Estimations obtain is followed successively by carrier coordinate system
The component of x, y, z axis direction, lxk-1、lyk-1、lzk-1The lever arm effect that k-1 epoch Kalman Filter Estimations obtain is followed successively by carry
The component of body coordinate system x, y, z axis direction.By lever arm if being compensated in Kalman filtering process lever arm effect
The corresponding Kalman filtering state vector corresponding entry zero setting of effect, otherwise not zero setting.
The prediction process of next epoch can be entered after step 4 is completed, above step just completes Kalman's filter
The renewal process of wave in entire navigation procedure, constantly carries out the cycle calculations of Kalman filtering, so as to entirely navigate through
Continuous reliably navigation in journey is provided and determines appearance information.
Claims (5)
1. a kind of GNSS/INS pine combinations Caused by Lever Arm estimation and compensation method, it is characterised in that include the following steps：
Step 1：Establish the Kalman filter model for including lever arm effect；
Step 2：The noise matrix of Kalman filtering of the setting comprising lever arm effect, the noise matrix of the Kalman filtering
Q gusts of the quantity of state noise matrix including reflecting inertial navigation noise level, P gusts of state vector variance matrix and measuring noise square difference
R gusts of matrix；
Step 3：The noise matrix of Kalman filtering using Kalman filter model and comprising lever arm effect is carried out comprising lever arm
The Kalman prediction of effect and update obtain including the state vector of lever arm effect error；
Step 4：Lever arm effect is compensated using the state vector comprising lever arm effect error.
2. a kind of GNSS/INS pine combinations Caused by Lever Arm estimation according to claim 1 and compensation method, it is characterised in that
Step 1 specifically includes following steps：
1.1 choose the state vector of the Kalman filtering comprising lever arm effect according to navigation system and navigation scenarios, described
Lever arm effect L=[lx ly lz], the state vector of the Kalman filtering comprising lever arm effect is：
Wherein L is vectorial for lever arm effect, x0To include the state vector of position, speed, posture and ins error, x is includes bar
The state vector of arm effect, lx、ly、lzFor lever arm under carrier coordinate system x, y, the residual error in z directions；
1.2 establish the state transition equation for the Kalman filtering for including lever arm effect：
xk=Φk,k-1xk-1+Γk-1Wk-1
In formula, xk,xk-1The respectively state vector at k and k-1 moment, Φk,k-1Be it is discrete after state-transition matrix, Γk-1For
System noise drives battle array, Wk-1For the noise vector of state, Φk,k-1It is expressed as：
In above formula, F0The corresponding state-transition matrix of Kalman filter equation not include lever arm effect, I matrixes are unit square
Battle array；
1.3 establish the measurement equation for the Kalman filtering for including lever arm effect
Z=Hx+V
In formula, Z matrixes are the measurement information matrix of Kalman filtering, and V is to measure noise matrix, and H-matrix is measurement equation coefficient
Matrix, wherein H-matrix form are as follows：
In above formula, H0The corresponding measurement equation coefficient matrix of Kalman filtering not include lever arm effect, in formulaWherein M represents meridian circle radius, and N represents prime vertical radius, and h represents the earth of carrier
Height,For the direction cosine matrix from body coordinate system to navigational coordinate system, l is the lever arm effect under body coordinate system, and m, n divide
It Wei not matrix line number and columns not comprising the Kalman filter model of lever arm effect.
3. a kind of GNSS/INS pine combinations Caused by Lever Arm estimation according to claim 1 and compensation method, it is characterised in that
The setting method of Q gusts of the quantity of state noise matrix of P gusts of state vector variance matrix in step 2 and reflection inertial navigation noise level
It is as follows：
Q gusts of settings of quantity of state noise matrix of Kalman filtering are as follows：
Wherein Q0The corresponding noise battle array of Kalman filtering not include lever arm effect, n are Kalman's filter not comprising lever arm effect
The dimension of the corresponding noise matrix of wave, QlIt is expressed as：
Wherein σlx、σly、σlzFor the error amount of lever arm effect, value 0.05；
P gusts of settings of state vector variance matrix of Kalman filtering are as follows：
Wherein, P0The corresponding noise battle array of Kalman filtering not include lever arm effect, PlIt is expressed as：
Wherein, σlx0、σly0、σlz0The uncertainty of lever arm effect initial value is represented, when lever arm effect initial value is set as zero,
The value is selected according to application scenarios.
4. a kind of GNSS/INS pine combinations Caused by Lever Arm estimation according to claim 2 and compensation method, it is characterised in that
Step 3 is specially：
The prediction process of Kalman filtering：
xk+1=Φkxk
Wherein, ΦkFor state-transition matrix, xk、xk+1The state vector at k moment and k+1 moment, Q are represented successivelykWhen representing k
The quantity of state noise matrix at quarter, Pk、Pk+1The state vector variance matrix at k moment and k+1 moment is represented successively；
The renewal process of Kalman filtering：
xk+1=xk+Kk(Zk-Hkxk)
Pk+1=(I-KkHk)Pk
Wherein KkRepresent the gain matrix at k moment, HkRepresent the measurement equation coefficient matrix at k moment, RkRepresent the measurement at k moment
Noise variance matrix, I represent unit matrix, and Z is the measurement information matrix at k moment；
Prediction and update are completed to have obtained including the state vector of lever arm effect error.
5. a kind of GNSS/INS pine combinations Caused by Lever Arm estimation according to claim 1 and compensation method, it is characterised in that
Step 4 is specially：
Lever arm effect is compensated using the state vector comprising lever arm effect error, obtains lever arm effect：
lxk=lxk-1+lx
lyk=lyk-1+ly
lzk=lzk-1+lz
In formula, lxk、lyk、lzkLever arm effect that k moment Kalman Filter Estimations obtain is followed successively by carrier coordinate system x, y, z axis
The component in direction, lxk-1、lyk-1、lzk-1Lever arm effect that k-1 moment Kalman Filter Estimations obtain is followed successively by carrier coordinate
It is the component of x, y, z axis direction, lx,ly,lzThe remnants being followed successively by lever arm effect x, y, the z directions of Kalman Filter Estimation are missed
Difference；By the corresponding Kalman filtering state of lever arm effect if being compensated in Kalman filtering process lever arm effect
Vectorial corresponding entry zero setting, otherwise not zero setting.
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| CN114111792A (en) * | 2021-11-22 | 2022-03-01 | 中国电子科技集团公司第五十四研究所 | Vehicle-mounted GNSS/INS/odometer combined navigation method |
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