CN108225312B - Lever arm estimation and compensation method in GNSS/INS loose combination - Google Patents

Lever arm estimation and compensation method in GNSS/INS loose combination Download PDF

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CN108225312B
CN108225312B CN201711438761.5A CN201711438761A CN108225312B CN 108225312 B CN108225312 B CN 108225312B CN 201711438761 A CN201711438761 A CN 201711438761A CN 108225312 B CN108225312 B CN 108225312B
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lever arm
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kalman filtering
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CN108225312A (en
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蔚保国
王青江
智奇楠
刘鹏飞
贾瑞才
马国驹
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CETC 54 Research Institute
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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
    • 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 lever arm estimation and compensation method in a GNSS/INS loose combination, which aims to solve the problems that: aiming at the problems that the measurement of the lever arm effect in a GNSS/INS loose integrated navigation system is inconvenient, and the navigation precision of the integrated navigation system is influenced due to the fact that the lever arm effect is constantly changed in the navigation process, a method for estimating the lever arm as a Kalman filtering state quantity is provided, the method does not need to determine the lever arm between an inertial navigation antenna and a satellite navigation antenna in advance, and therefore the measurement process of the lever arm before navigation is avoided, and besides, the problem that the error of the lever arm is changed in real time due to vibration of a carrier in the navigation process can be effectively compensated.

Description

Lever arm estimation and compensation method in GNSS/INS loose combination
Technical Field
The invention relates to the field of GNSS/INS integrated navigation, in particular to a method for estimating and compensating a lever arm effect caused by the fact that the installation positions of a GNSS antenna and an INS are not coincident in a GNSS/INS integrated navigation system through a Kalman filtering algorithm.
Background
When the observation condition is good, the GNSS equipment works alone to obtain a reliable navigation result. However, in severe observation conditions such as cities, forests and canyons where a high-rise building stands, when the number of visible satellites is less than four, the GNSS cannot perform navigation solution. The INS has high information updating frequency, and after initialization is completed, the position, speed, attitude and other information of the carrier can be calculated by means of the angular velocity and specific force information measured by the INS, however, the navigation positioning resolving accuracy is dispersed along with time due to the influence of error accumulation. The GNSS and the INS have good complementarity, and the combination of the two can provide more accurate and reliable navigation positioning results compared to a single system. In the GNSS/INS combined navigation, the GNSS provides the updating information required by inertial navigation, so that the divergence of inertial navigation information is inhibited, the inertial navigation can output navigation positioning information with high sampling rate, and when the GNSS is interrupted due to the shielding or interference of signals, the inertial navigation can still continue to work, so that the reliability and the robustness of the system are improved.
In practical navigation applications, inertial navigation is usually fixed inside a carrier in order to make inertial navigation accurately reflect the attitude of the carrier, and a receiver antenna is usually mounted on the top of the carrier in order to obtain a good observation signal. The lever arm effect is generated due to the fact that inertial navigation and satellite navigation antennas are installed in different positions. In order to obtain a high accuracy of the combined navigation result, compensation of the lever arm effect has to be performed. In addition, for some large carriers, the lever arm is not constant but in a real-time changing state due to the existence of vibration in application, so that the error of the lever arm is determined to be a fixed constant value, and the error of the navigation estimation can be introduced into the navigation estimation. Therefore, effective compensation of the lever arm effect is a key step to improve navigation accuracy.
Disclosure of Invention
The invention aims to solve the problems that: aiming at the problems that the measurement of the lever arm effect in a GNSS/INS loose integrated navigation system is inconvenient, and the navigation precision of the integrated navigation system is influenced due to the fact that the lever arm effect is constantly changed in the navigation process, a method for estimating the lever arm as a Kalman filtering state quantity is provided, the method does not need to determine the lever arm between an inertial navigation antenna and a satellite navigation antenna in advance, and therefore the measurement process of the lever arm before navigation is avoided, and besides, the problem that the error of the lever arm is changed in real time due to vibration of a carrier in the navigation process can be effectively compensated.
The invention comprises the following contents:
a lever arm estimation and compensation method in a GNSS/INS loose combination comprises the following steps:
the method comprises the following steps: establishing a Kalman filtering model containing a lever arm effect;
step two: setting a Kalman filtering noise matrix comprising a lever arm effect, wherein the Kalman filtering noise matrix comprises a state quantity noise matrix Q matrix reflecting the inertial navigation noise level, a state vector variance matrix P matrix and a measurement noise matrix R matrix;
step three: performing Kalman filtering prediction and updating including a lever arm effect by using a Kalman filtering model and a Kalman filtering noise matrix including the lever arm effect to obtain a state vector including a lever arm effect error;
step four: the lever arm effect is compensated for using a state vector that contains the error of the lever arm effect.
The first step specifically comprises the following steps:
1.1 selecting a Kalman filtering state vector containing a lever arm effect according to a navigation system and a navigation scene, wherein the lever arm effect L is Lxlylz]The state vector of kalman filtering, including the lever arm effect, is:
Figure BDA0001526260520000031
wherein L is the lever arm effect vector, x0Is a state vector containing position, velocity, attitude and inertial navigation errors, x is a state vector containing lever arm effects, lx、ly、lzResidual errors of the lever arm in the x, y and z directions under a carrier coordinate system are obtained;
1.2 establishing a state transition equation of Kalman filtering comprising a lever arm effect:
xk＝Φk,k-1xk-1+Γk-1Wk-1
in the formula, xk,xk-1State vectors at times k and k-1, respectively, phik,k-1For discrete state transition matrices, Γk-1For system noise-driven arrays, Wk-1As noise vector of state, phik,k-1Expressed as:
Figure BDA0001526260520000032
in the above formula, F0A state transition matrix corresponding to a Kalman filtering equation without a lever arm effect is adopted, and an I matrix is an identity matrix;
1.3 establishing a measurement equation for Kalman filtering including the Lever arm Effect
Z＝Hx+V
In the formula, the Z matrix is a measurement information matrix of kalman filtering, V is a measurement noise item, a noise variance matrix thereof is represented by an R matrix, and the H matrix is a measurement equation coefficient matrix, wherein the H matrix has the following form:
Figure BDA0001526260520000033
in the above formula, H0A matrix of measurement equation coefficients corresponding to Kalman filtering without lever arm effect, wherein
Figure BDA0001526260520000034
Wherein M represents the radius of meridian, N represents the radius of unitary mortise, h represents the height of the carrier,
Figure BDA0001526260520000035
the direction cosine matrix from the body coordinate system to the navigation coordinate system, l is the lever arm effect under the body coordinate system, and m and n are the matrix row number and column number of the Kalman filtering model without the lever arm effect respectively.
The setting method of the state vector initial uncertainty matrix P array and the state vector noise matrix Q array reflecting the inertial navigation noise level in the step two is as follows:
the state quantity noise matrix Q array of Kalman filtering is set as follows:
Figure BDA0001526260520000041
wherein Q0Noise matrix, Q, for Kalman filtering without lever arm effectlExpressed as:
Figure BDA0001526260520000042
wherein sigmalx、σly、σlzThe value is 0.05 for the error value of the lever arm effect;
the initial uncertainty matrix P array of the state vector of Kalman filtering is set as follows:
wherein, P0Initial value uncertainty of state vector for Kalman filtering without lever arm effect, PlExpressed as:
Figure BDA0001526260520000044
wherein σlx0、σly0、σlz0Representing the uncertainty of the lever arm effect initial value, which is selected according to the application scenario when it is set to zero.
Wherein, the third step is specifically as follows:
prediction process of Kalman filtering:
xk+1＝Φkxk
Figure BDA0001526260520000045
wherein phikIs a state transition matrix, xk、xk+1Representing the state vectors at time k and at time k +1, Q, in that orderkRepresenting the state quantity noise matrix at time k, Pk、Pk+1Sequentially representing state vector variance matrixes at the k moment and the k +1 moment;
updating process of Kalman filtering:
Figure BDA0001526260520000051
xk+1＝xk+Kk(Zk-Hkxk)
Pk+1＝(I-KkHk)Pk
wherein KkRepresenting the gain matrix at time k, HkCoefficient matrix of measurement equation representing time k, RkRepresenting a measurement noise matrix, I representing a unit matrix, and Z representing a measurement information matrix at the moment k;
the prediction and update are done resulting in a state vector containing the lever arm effect error.
Wherein, the step four is specifically as follows:
compensating the lever arm effect by using the state vector containing the lever arm effect error to obtain the lever arm effect:
lxk＝lxk-1+lx
lyk＝lyk-1+ly
lzk＝lzk-1+lz
in the formula, lxk、lyk、lzkSequentially obtaining components of lever arm effect in x, y and z axis directions of a carrier coordinate system, lx, obtained by k moment Kalman filtering estimationk-1、lyk-1、lzk-1Sequentially obtaining the components l of the lever arm effect obtained by k-1 moment Kalman filtering estimation in the directions of x, y and z axes of a carrier coordinate systemx,ly,lzSequentially estimating residual errors in the x, y and z directions of the lever arm effect estimated by Kalman filtering; and if the lever arm effect is compensated in the Kalman filtering process, zeroing the corresponding item of the Kalman filtering state vector corresponding to the lever arm effect, otherwise, not zeroing.
The steps complete the updating process of the Kalman filtering once, and the circular calculation of the Kalman filtering is continuously carried out in the whole navigation process, so that the continuous and reliable navigation attitude determination information is provided in the whole navigation process.
The invention has the advantages that:
the method and the device take the lever arm effect value as the state vector of Kalman filtering for estimation, thereby avoiding the measurement of the lever arm value before real-time navigation, effectively improving the navigation efficiency, and simultaneously avoiding the navigation error caused by the continuous change of the lever arm value due to the vibration in the motion process of a carrier.
Drawings
FIG. 1 is a Kalman filtering architecture block diagram.
Fig. 2 is a schematic diagram of lever arm effect.
Detailed Description
The invention will be further described with reference to specific embodiments and the accompanying drawings in which:
as shown in fig. 1, the present invention mainly comprises four steps, which are as follows:
the method comprises the following steps: and establishing a Kalman filtering model containing a lever arm effect. The substeps are as follows:
1.1 selecting a kalman filter state vector according to a scene of a navigation application, generally, the more the selected state quantity is, the more accurately a motion model can be reflected, the more accurately the state quantity can be estimated, and in addition, the selection of the state quantity also depends on a used inertial navigation grade, for example, for a low-grade MEMS inertial navigation, a scale factor and a quadrature axis coupling error of the MEMS inertial navigation are large, and the state quantity needs to be comprehensively considered when being selected, however, the complexity of calculation increases along with the increase of the state quantity, so that the state quantity needs to be comprehensively considered when being selected, and in this embodiment, a total of 18 errors including a position error, a velocity error, an attitude error, a gyro zero offset error, an accelerometer zero offset error and a lever arm error are selected as the state quantity. The state quantities are as follows:
Figure BDA0001526260520000061
wherein δ rNδrEδrDRepresents a positional error in the northeast direction, δ vNδvEδvDRepresenting the velocity error in the northeast direction,. phiNψEψDRepresenting roll, pitch, course angle errors, bgxbgybgzRepresenting zero offset error of gyroscope x, y, z axis, baxbaybazRepresents the zero offset error of the x, y and z axes of the accelerometer, and the delta lx delta ly delta lz represents the error of the lever arm effect in the x, y and z directions in a carrier coordinate system.
1.2 establishing a state transition equation of Kalman filtering comprising a lever arm effect:
xk＝Φk,k-1xk-1+Γk-1Wk-1
in the formula, xk,xk-1State vectors at times k and k-1, respectively, phik,k-1For discrete state transition matrices, Γk-1For system noise-driven arrays, Wk-1As noise vector of state, phik,k-1Expressed as:
in this embodiment, a state transition matrix corresponding to 18 state quantities, including a position error, a velocity error, an attitude error, a gyro zero-offset error, an accelerometer zero-offset error, and a lever arm error, is selected as follows:
Figure BDA0001526260520000071
wherein:
Figure BDA0001526260520000072
Figure BDA0001526260520000073
Figure BDA0001526260520000074
Figure BDA0001526260520000081
Figure BDA0001526260520000082
Figure BDA0001526260520000083
wherein v isE、vN、vDRepresenting in turn the east, north and sky velocities of the carrier, ωeRepresenting the self-propagating angular velocity of the earth, M, N and h sequentially representing the radius of the unitary fourth-earth orbit, the radius of the meridian and the ground height of the carrier,
Figure BDA0001526260520000084
representing the latitude of the carrier, gamma representing the normal gravity value of the local area, delta T, TabRepresenting the sampling interval and the correlation time of the inertial navigation noise. f. ofb,fnRepresenting the projection of the sensor output in the carrier coordinate system and the navigation coordinate system.
1.3 establishing a measurement equation for Kalman filtering including the Lever arm Effect
Zk＝Hkxk+Vk
In the above formula, the Z matrix represents a measurement information matrix of kalman filtering, the V matrix represents a measurement noise item, and the H matrix represents a measurement equation coefficient matrix, wherein the H matrix has the following form:
Figure BDA0001526260520000085
where l represents the lever arm value and,
Figure BDA0001526260520000086
representing a direction cosine matrix from the carrier coordinate system to the navigation coordinate system,
Figure BDA0001526260520000087
is the projection of the carrier motion relative to the inertial system in the carrier coordinate system,
Figure BDA0001526260520000088
for the projection of the navigation coordinate system onto the navigation coordinate system for the motion of the navigation coordinate system relative to the terrestrial coordinate system,
Figure BDA0001526260520000089
is a projection of the terrestrial coordinate system relative to the inertial coordinate system in the navigational coordinate system.
The variance matrix R matrix of the measurement noise terms is expressed as follows:
Figure BDA0001526260520000091
wherein
Figure BDA0001526260520000092
The GNSS observation information comprises an east position variance value, a north position variance value, an sky position variance value, an east speed variance value, a north speed variance value and an sky speed variance value.
Step two: and setting a noise matrix of Kalman filtering. The Kalman filtering noise matrix comprises an updating equation noise Q matrix, an initial state quantity uncertainty matrix P matrix and a measurement noise matrix R matrix.
2.1 the Q-matrix for Kalman filtering is set as follows:
Qk＝diag{0 0 0 vrw2vrw2vrw2arw2arw2arw2QgbQgbQgbQabQabQabσlxσlyσlz}
vrw represents the velocity random walk of the inertial sensor, arw represents the angular random walk of the inertial sensor, Qgb，QabWhich in turn represents the output noise of the inertial sensor.
2.2 the measurement noise matrix of Kalman filtering is as follows:
Figure BDA0001526260520000093
2.3 initial value of P matrix of Kalman Filter reflects initial uncertainty of state vector, and initial value P of P matrix0The settings were as follows:
Figure BDA0001526260520000094
step three: kalman filtering prediction and update processes.
Prediction process of Kalman filtering:
xk+1＝Φkxk
Figure BDA0001526260520000101
wherein phikIs a state transition matrix, xk、xk+1Representing the state vectors at time k and at time k +1, Q, in that orderkRepresenting the state quantity noise matrix at time k, Pk、Pk+1Representing the state vector variance matrix at time k and at time k +1 in that order.
Updating process of Kalman filtering:
Figure BDA0001526260520000102
xk+1＝xk+Kk(Zk-Hkxk)
Pk+1＝(I-KkHk)Pk
wherein KkRepresenting the gain matrix at time k, HkCoefficient matrix of measurement equation representing time k, RkRepresents the measured noise matrix at time k, and I represents the identity matrix.
Step four: and compensating the feedback.
After Kalman filtering updating, a state vector containing a lever arm effect error is estimated, and then the lever arm effect can be obtained:
lxk＝lxk-1+lx
lyk＝lyk-1+ly
lzk＝lzk-1+lz
in the above formula lxk、lyk、lzkSequentially obtaining the components of the lever arm effect in the x, y and z axis directions of the carrier coordinate system, lx, obtained by k epoch Kalman filtering estimationk-1、lyk-1、lzk-1Sequentially obtaining the components of the lever arm effect obtained by k-1 epoch Kalman filtering estimation in the x, y and z axis directions of the carrier coordinate system. And if the lever arm effect is compensated in the Kalman filtering process, zeroing the corresponding item of the Kalman filtering state vector corresponding to the lever arm effect, otherwise, not zeroing.
And after the step four is completed, the prediction process of the next epoch can be entered, the above steps complete the updating process of the Kalman filtering once, and the circular calculation of the Kalman filtering is continuously carried out in the whole navigation process, so that the continuous and reliable navigation attitude determination information is provided in the whole navigation process.

Claims (4)

1. A lever arm estimation and compensation method in a GNSS/INS loose combination is characterized by comprising the following steps:
the method comprises the following steps: establishing a Kalman filtering model containing a lever arm effect;
step two: setting a Kalman filtering noise matrix comprising a lever arm effect, wherein the Kalman filtering noise matrix comprises a state quantity noise matrix Q matrix reflecting the inertial navigation noise level, a state vector variance matrix P matrix and a measurement noise variance matrix R matrix;
step three: performing Kalman filtering prediction and updating including a lever arm effect by using a Kalman filtering model and a Kalman filtering noise matrix including the lever arm effect to obtain a state vector including a lever arm effect error;
step four: compensating the lever arm effect by using a state vector containing the lever arm effect error;
the first step specifically comprises the following steps:
1.1 selecting a Kalman filtering state vector containing a lever arm effect according to a navigation system and a navigation scene, wherein the lever arm effect L is Lxlylz]The state vector of kalman filtering, including the lever arm effect, is:
Figure FDA0002418626820000011
the method specifically comprises the following steps:
Figure FDA0002418626820000012
wherein L is lever arm effect vector, x0Is a state vector containing position, velocity, attitude and inertial navigation errors, x is a state vector containing lever arm effects, lx、ly、lzResidual errors of the lever arm in the x, y and z directions under a carrier coordinate system are obtained; delta rNδrEδrDRepresents a positional error in the northeast direction, δ vNδvEδvDRepresenting the velocity error in the northeast direction,. phiNψEψDRepresenting roll, pitch, course angle errors,
Figure FDA0002418626820000013
represents the zero offset error of the x, y and z axes of the gyroscope,
Figure FDA0002418626820000014
representing zero offset errors of x, y and z axes of the accelerometer, and representing errors of a lever arm effect in x, y and z directions in a carrier coordinate system by delta lx delta ly delta lz;
1.2 establishing a state transition equation of Kalman filtering comprising a lever arm effect:
xk＝Φk,k-1xk-1+Γk-1Wk-1
in the formula, xk,xk-1State vectors at times k and k-1, respectively, phik,k-1For discrete state transition matrices, Γk-1For system noise-driven arrays, Wk-1As noise vector of state, phik,k-1Expressed as:
Figure FDA0002418626820000021
the state transition matrix is specifically:
Figure FDA0002418626820000022
wherein the content of the first and second substances,
Figure FDA0002418626820000023
Figure FDA0002418626820000024
Figure FDA0002418626820000025
Figure FDA0002418626820000031
Figure FDA0002418626820000032
in the formula, F0A state transition matrix corresponding to a Kalman filtering equation without lever arm effect, wherein the matrix I is an identity matrix, and v isE、vN、vDRepresenting in turn the east, north and sky velocities of the carrier, ωeRepresenting the self-propagating angular velocity of the earth, M, N and h sequentially representing the radius of the unitary fourth-earth orbit, the radius of the meridian and the ground height of the carrier,
Figure FDA0002418626820000033
representing the latitude of the carrier, gamma representing the normal gravity value of the local area, delta T, TabRepresenting the sampling interval and the correlation time of the inertial navigation noise, fb,fnRepresenting the projection of the sensor output in a carrier coordinate system and a navigation coordinate system;
1.3 establishing a measurement equation for Kalman filtering including the Lever arm Effect
Z＝Hx+V
In the formula, the Z matrix is a measurement information matrix of kalman filtering, V is a measurement noise matrix, and the H matrix is a measurement equation coefficient matrix, wherein the H matrix has the following form:
Figure FDA0002418626820000034
in the above formula, H0A matrix of measurement equation coefficients corresponding to Kalman filtering without lever arm effect, wherein
Figure FDA0002418626820000035
Wherein M represents the radius of meridian, N represents the radius of unitary mortise, h represents the height of the carrier,
Figure FDA0002418626820000036
the direction cosine matrix from the body coordinate system to the navigation coordinate system, l is the lever arm effect under the body coordinate system, and m and n are the matrix row number and column number of the Kalman filtering model without the lever arm effect respectively.
2. The method as claimed in claim 1, wherein the method for estimating and compensating lever arm in GNSS/INS pine combination comprises the following steps:
the state quantity noise matrix Q array of Kalman filtering is set as follows:
Figure FDA0002418626820000041
wherein Q0A noise matrix corresponding to Kalman filtering without lever arm effect, n is the dimension of the noise matrix corresponding to Kalman filtering without lever arm effect,Qlexpressed as:
Figure FDA0002418626820000042
wherein sigmalx、σly、σlzThe value is 0.05 for the error value of the lever arm effect;
the state vector variance matrix P matrix of Kalman filtering is set as follows:
Figure FDA0002418626820000043
wherein, P0Noise arrays, P, corresponding to Kalman filtering, not involving lever arm effectslExpressed as:
Figure FDA0002418626820000044
wherein σlx0、σly0、σlz0Representing the uncertainty of the lever arm effect initial value, which is selected according to the application scenario when it is set to zero.
3. The method as claimed in claim 1, wherein the step three comprises:
prediction process of Kalman filtering:
xk+1＝Φkxk
Figure FDA0002418626820000045
wherein phikIs a state transition matrix, xk、xk+1Representing the state vectors at time k and at time k +1, Q, in that orderkRepresenting the state quantity noise matrix at time k, Pk、Pk+1Sequentially representing state vector variance matrixes at the k moment and the k +1 moment;
updating process of Kalman filtering:
Figure FDA0002418626820000051
xk+1＝xk+Kk(Zk-Hkxk)
Pk+1＝(I-KkHk)Pk
wherein KkRepresenting the gain matrix at time k, HkCoefficient matrix of measurement equation representing time k, RkRepresenting a measurement noise variance matrix at the moment k, I representing a unit matrix, and Z representing a measurement information matrix at the moment k;
the prediction and update are done resulting in a state vector containing the lever arm effect error.
4. The method as claimed in claim 1, wherein the step four comprises:
compensating the lever arm effect by using the state vector containing the lever arm effect error to obtain the lever arm effect:
lxk＝lxk-1+lx
lyk＝lyk-1+ly
lzk＝lzk-1+lz
in the formula, lxk、lyk、lzkSequentially obtaining components of lever arm effect in x, y and z axis directions of a carrier coordinate system, lx, obtained by k moment Kalman filtering estimationk-1、lyk-1、lzk-1Sequentially obtaining the components l of the lever arm effect obtained by k-1 moment Kalman filtering estimation in the directions of x, y and z axes of a carrier coordinate systemx,ly,lzSequentially estimating residual errors in the x, y and z directions of the lever arm effect estimated by Kalman filtering; and if the lever arm effect is compensated in the Kalman filtering process, zeroing the corresponding item of the Kalman filtering state vector corresponding to the lever arm effect, otherwise, not zeroing.
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