CN115096303A - GNSS multi-antenna and INS tightly-combined positioning and attitude determination method and equipment - Google Patents

GNSS multi-antenna and INS tightly-combined positioning and attitude determination method and equipment Download PDF

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CN115096303A
CN115096303A CN202211024566.9A CN202211024566A CN115096303A CN 115096303 A CN115096303 A CN 115096303A CN 202211024566 A CN202211024566 A CN 202211024566A CN 115096303 A CN115096303 A CN 115096303A
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vector
matrix
antenna
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observation
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CN115096303B (en
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余文坤
李鑫
戴吾蛟
潘林
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Central South 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
    • 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

Abstract

The invention discloses a GNSS multi-antenna and INS tightly combined positioning and attitude determining method and equipment, wherein the method comprises the following steps: constructing a double-difference carrier and double-difference pseudorange rate measurement equation represented by a position vector and a velocity vector at an inertial navigation center through a lever arm vector and a rotation matrix; considering the correlation when the multi-antenna GNSS observation values form double-difference observation values, and constructing a covariance matrix of the observation values of the GNSS multi-antenna and INS tight combination system by using an error propagation law; according to the double-difference carrier wave, the double-difference pseudo range rate equation and the covariance matrix, a measurement equation based on variable correction of a tight combination system is constructed; and taking errors such as position, speed, attitude and the like as state vectors of the system, establishing a system state equation by adopting a first-order Gaussian Markov process, and carrying out Kalman filtering solution to obtain the optimal estimation of the position, the speed and the attitude of the inertial navigation center at each moment. The invention has high stability and precision of positioning and attitude determination.

Description

GNSS multi-antenna and INS tightly-combined positioning and attitude determination method and equipment
Technical Field
The invention belongs to the technical field of navigation positioning, and particularly relates to a GNSS multi-antenna and INS tightly-combined positioning and attitude determination method and equipment.
Background
Accurate and reliable information such as position and attitude plays a key role in carrier Navigation, guidance and control, and GNSS (Global Navigation Satellite System) and INS (Inertial Navigation System) are two main means for acquiring pose information. GNSS systems can provide high-precision positioning and navigation services to users on a global scale, but they are susceptible to interference in a dynamic environment causing loss of lock of satellite signals, resulting in unusable positioning results. The INS system has strong autonomy and anti-jamming capability, but the result of each moment is recurred from the previous moment, and errors can be accumulated along with time when the INS system works for a long time, so that the navigation result is unreliable. At present, the two systems are often combined to perform positioning and attitude determination so as to improve the stability and reliability of the navigation system.
The existing GNSS and INS positioning and attitude determination methods have the technical problems that:
the patent scheme with publication number CN103245963A provides a dual-antenna GNSS/INS deep integrated navigation method and device, which use the attitude of dual-antenna GNSS differential solution to constrain the attitude of the INS system. However, the attitude constraint by the baseline combination resolved by the dual-antenna GNSS differential belongs to a loose combination, data is not fully utilized, the anti-interference capability is poor, and the ambiguity of the baseline vector needs to be fixed at first, if the ambiguity cannot be fixed or is fixed by mistake, the error is brought into the computed attitude, and the final navigation result is influenced.
The patent scheme with the publication number of CN114252077A provides a combined navigation method and system of dual-antenna GPS/SINS based on a federal filter, which uses the federal filter to combine the observations of two GPS systems with INS respectively for filtering, so as to improve the robustness of the system, but the scheme also uses a loose combination mode for the combination of GPS and INS, and the anti-interference capability and the resolution precision are not as good as those of the tight combination mode.
The Chaihuaju et al provides a multi-antenna GNSS/INS combined navigation algorithm and result analysis (Chaihuaju, Hushuai, Stallmin. the multi-antenna GNSS/INS combined navigation algorithm and result analysis [ C ],2021: 146-.
In the combined positioning and attitude determination problem of the GNSS and the INS, how to design a reasonable function model and fully and effectively utilize redundant observation information of a plurality of antennas is a key problem. The traditional solution is to first solve the baseline vector between the master antenna and the slave antenna, and establish the measurement equation of the combination of the multi-GNSS antenna and the INS using the relation between the baseline vector and the attitude of the carrier, but this approach usually belongs to a loose combination and depends heavily on the correct fixation of the whole-cycle ambiguity.
Disclosure of Invention
Aiming at the problem of combined positioning and attitude determination of the GNSS and the INS, the invention provides a method and equipment for tightly combining positioning and attitude determination of the GNSS multi-antenna and the INS.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a GNSS multi-antenna and INS tightly combined positioning and attitude determination method comprises the following steps:
step 1, normalizing coordinate parameters of a plurality of GNSS antennas to inertial navigation center coordinate parameters through a lever arm vector and a rotation matrix, and constructing a double-difference carrier and double-difference pseudo-range rate measurement equation represented by a position vector and a speed vector at an inertial navigation center;
step 2, considering the correlation when the multi-antenna GNSS observation values form a double-difference observation value, and constructing a covariance matrix of the observation values of the GNSS multi-antenna and INS tight combination system by using an error propagation law;
step 3, constructing and obtaining a variable correction number-based measurement equation of the GNSS multi-antenna and INS tight combination system according to the double-difference carrier wave and double-difference pseudo range rate measurement equation obtained in the step 1 and the multi-antenna observation covariance matrix obtained in the step 2;
step 4, taking the position, the speed, the attitude, the zero offset of the sensor and the error of the scale factor at the inertial navigation center as the state vector of the system, and establishing a system state equation by adopting a first-order Gaussian Markov process;
and 5, performing Kalman filtering solution according to the measurement equation and the system state equation to obtain the optimal estimation of the position, the speed and the attitude of the inertial navigation center at each moment.
Further, the method for normalizing the coordinate parameters of the GNSS antenna to the inertial navigation center coordinate parameters comprises:
Figure DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE002
、
Figure DEST_PATH_IMAGE003
respectively representing antennas
Figure DEST_PATH_IMAGE004
The position vector and the velocity vector of (c),
Figure DEST_PATH_IMAGE005
、vrespectively representing a position vector and a velocity vector of an inertial navigation center;
Figure DEST_PATH_IMAGE006
is a direction cosine matrix, i.e. a rotation matrix;
Figure DEST_PATH_IMAGE007
is an antenna
Figure 472470DEST_PATH_IMAGE004
The lever arm vector of (a);
Figure DEST_PATH_IMAGE008
is the three-dimensional angular velocity of the IMU output
Figure DEST_PATH_IMAGE009
Of an anti-symmetric matrix, i.e.
Figure DEST_PATH_IMAGE010
，
Figure DEST_PATH_IMAGE011
Is an antisymmetric array operator;
Figure DEST_PATH_IMAGE012
is an antisymmetric matrix of the rotational angular velocity of the earth.
Further, a double difference carrier and double difference pseudorange rate equation expressed in a position vector and a velocity vector at the inertial navigation center is constructed, expressed as:
Figure DEST_PATH_IMAGE013
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE014
is an antenna
Figure 717506DEST_PATH_IMAGE004
A single difference sight line vector matrix between the satellites, which is
Figure DEST_PATH_IMAGE015
A matrix of dimensions is formed by a matrix of dimensions,
Figure DEST_PATH_IMAGE016
subtracting the number of the adopted satellite systems from the total number of the observation satellites;
Figure DEST_PATH_IMAGE017
the amount of the carbon dioxide is the intermediate amount,
Figure DEST_PATH_IMAGE018
is a non-zero diagonal array of corresponding carrier wavelengths,
Figure DEST_PATH_IMAGE019
antenna for representation
Figure DEST_PATH_IMAGE020
Double difference observation noise between the two;
Figure DEST_PATH_IMAGE021
antenna for representation
Figure 575872DEST_PATH_IMAGE020
The two-difference carrier observations in between,
Figure DEST_PATH_IMAGE022
antenna for representation
Figure 502239DEST_PATH_IMAGE020
Double-differenced pseudorange rate observations between.
Further, the measurement equation obtained in step 3 is expressed as:
Figure DEST_PATH_IMAGE023
wherein, the first and the second end of the pipe are connected with each other,
Figure DEST_PATH_IMAGE024
represents the number of corrections of the variable;
Figure DEST_PATH_IMAGE025
the observation vector representing the GNSS antenna combined system comprises the carrier wave and the pseudo range rate observed by the GNSS system,
Figure DEST_PATH_IMAGE026
representing observation vectors
Figure 365547DEST_PATH_IMAGE025
The correction number of the inertial navigation system is obtained by subtracting the carrier wave and the pseudo-range rate of the GNSS and the carrier wave and the pseudo-range rate calculated by the inertial navigation;
Figure DEST_PATH_IMAGE027
representing state vectors
Figure DEST_PATH_IMAGE028
Correcting;
Figure 100002_DEST_PATH_IMAGE029
indicating the number of corrections of the observation vector
Figure 984747DEST_PATH_IMAGE026
And state vector correction number
Figure 517359DEST_PATH_IMAGE027
A matrix of relationships between;
Figure DEST_PATH_IMAGE030
representing white noise;
Figure DEST_PATH_IMAGE031
a covariance matrix representing the observations;
state vector
Figure 247418DEST_PATH_IMAGE028
Comprises the following steps:
Figure DEST_PATH_IMAGE032
wherein the content of the first and second substances,
Figure 181876DEST_PATH_IMAGE005
determining a carrier three-dimensional position vector as an inertial navigation reference center;
Figure DEST_PATH_IMAGE033
representing a velocity vector;
Figure DEST_PATH_IMAGE034
representing a pose vector;
Figure DEST_PATH_IMAGE035
represents the accelerometer zero offset;
Figure DEST_PATH_IMAGE036
represents a gyro zero bias;
Figure DEST_PATH_IMAGE037
representing an accelerometer scale factor;
Figure DEST_PATH_IMAGE038
represents a gyro scale factor;
Figure DEST_PATH_IMAGE039
representing a double difference ambiguity vector.
Further, the observation vector is corrected
Figure 253868DEST_PATH_IMAGE026
And a matrix of associations
Figure 273777DEST_PATH_IMAGE029
Respectively as follows:
Figure DEST_PATH_IMAGE040
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE041
a main antenna is shown, which is,
Figure DEST_PATH_IMAGE042
to represent
Figure DEST_PATH_IMAGE043
A plurality of auxiliary antennas are arranged on the base plate,
Figure DEST_PATH_IMAGE044
to represent
Figure DEST_PATH_IMAGE045
A reference station;
Figure 100002_DEST_PATH_IMAGE046
denotes a subscript
Figure DEST_PATH_IMAGE047
A double-difference carrier observation between them,
Figure DEST_PATH_IMAGE048
denotes a subscript
Figure 853532DEST_PATH_IMAGE047
Double-difference pseudorange rate observations between;
Figure DEST_PATH_IMAGE049
represent a subscript
Figure DEST_PATH_IMAGE050
A matrix of associations between the associated double difference vector corrections and the state vector corrections, and having:
Figure DEST_PATH_IMAGE051
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE052
to represent
Figure 100002_DEST_PATH_IMAGE053
A zero matrix of the dimensions is formed,
Figure DEST_PATH_IMAGE054
for non-zero diagonal arrays of corresponding carrier wavelengths, intermediate variables
Figure DEST_PATH_IMAGE055
The specific expression of (A) is as follows:
Figure 100002_DEST_PATH_IMAGE056
。
further, a covariance matrix of the observation values of the GNSS multi-antenna and INS tight combination system is constructed by using an error propagation lawRThe method comprises the following steps:
first, the antenna is installed
Figure 252283DEST_PATH_IMAGE020
And satellite
Figure DEST_PATH_IMAGE057
,
Figure 213286DEST_PATH_IMAGE045
The double difference between the observed values is expressed as
Figure DEST_PATH_IMAGE058
Will be arbitrary antenna
Figure 720491DEST_PATH_IMAGE004
For any satellite
Figure 995614DEST_PATH_IMAGE057
Is expressed as
Figure DEST_PATH_IMAGE059
Then the original non-differential observed value can be obtained from the law of error propagation
Figure 416581DEST_PATH_IMAGE059
And double difference observed value
Figure 17327DEST_PATH_IMAGE058
The relationship between them is:
Figure DEST_PATH_IMAGE060
then, the conversion matrix is calculated according to the relational expression
Figure DEST_PATH_IMAGE061
Comprises the following steps:
Figure DEST_PATH_IMAGE062
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE063
to represent
Figure DEST_PATH_IMAGE064
A zero matrix of the dimensions is formed,
Figure DEST_PATH_IMAGE065
the specific expression of (A) is as follows:
Figure DEST_PATH_IMAGE066
finally, according to the transformation matrix
Figure 74145DEST_PATH_IMAGE061
And covariance matrix of original non-differential observations
Figure DEST_PATH_IMAGE067
Determining the covariance matrix of the combined system observations as:
Figure DEST_PATH_IMAGE068
。
further, the observation vector is corrected
Figure 434850DEST_PATH_IMAGE026
The calculation method comprises the following steps: calculating a double-difference carrier observed value and a double-difference pseudo range rate observed value according to position, speed and attitude information updated by an inertial navigation center and a satellite ephemeris; and (4) subtracting the carrier wave and the pseudo-range rate obtained by the observation of the GNSS system, and using the difference as the correction number of the observation vector in the measurement equation.
Further, a double-difference observation equation is constructed according to the observation value of the multi-antenna GNSS system, the position, the speed and the attitude information of the combined system are obtained by resolving the double-difference observation equation, and the information is used for initializing the inertial navigation center.
Further, the state equation of the system established by adopting the first-order Gaussian Markov process is as follows:
Figure DEST_PATH_IMAGE069
wherein
Figure DEST_PATH_IMAGE070
Is a state vector
Figure 463986DEST_PATH_IMAGE028
At the moment of time
Figure DEST_PATH_IMAGE071
The superscript "-" indicates that a variable has not been updated by the most recent observation, and once updated, the corresponding superscript will become "+";
Figure DEST_PATH_IMAGE072
in order to be a state transition matrix,
Figure DEST_PATH_IMAGE073
for the process noise vector, assuming a normal distribution obeying zero mean,
Figure DEST_PATH_IMAGE074
is a transfer matrix for the process noise,
Figure DEST_PATH_IMAGE075
a covariance matrix that is the process noise;
Figure 297950DEST_PATH_IMAGE072
the specific expression of (A) is as follows:
Figure DEST_PATH_IMAGE076
Figure DEST_PATH_IMAGE077
Figure DEST_PATH_IMAGE078
wherein the state transition matrix
Figure 29014DEST_PATH_IMAGE072
3 in each element subscript in (a) denotes a 3 × 3 matrix, n denotes an n × n matrix, 3 × n denotes a 3 row by n column matrix, and n × 3 denotes an n row by 3 column matrix;
Figure 177099DEST_PATH_IMAGE005
the three-dimensional position vector of the inertial navigation center is obtained;
Figure DEST_PATH_IMAGE079
the distance between the earth surface and the earth center;
Figure DEST_PATH_IMAGE080
is a gravity vector;
Figure DEST_PATH_IMAGE081
is the three-dimensional specific force vector output by the accelerometer;
Figure 60741DEST_PATH_IMAGE009
a three-dimensional angular velocity output for the IMU;
Figure DEST_PATH_IMAGE082
to be composed of
Figure DEST_PATH_IMAGE083
A diagonal matrix being diagonal elements;
Figure DEST_PATH_IMAGE084
are all intermediate variables;
Figure DEST_PATH_IMAGE085
for the correlation time of the accelerometer zero offset,
Figure DEST_PATH_IMAGE086
is the relative time of the gyro zero offset,
Figure DEST_PATH_IMAGE087
is the correlation time of the accelerometer scale factor,
Figure DEST_PATH_IMAGE088
the correlation time of the gyro scale factor;
Figure DEST_PATH_IMAGE089
measuring time intervals for the accelerometer and gyroscope;
Figure DEST_PATH_IMAGE090
is an antisymmetric matrix of the rotational angular velocity of the earth;
the specific recursion calculation formula for performing Kalman filtering solution according to the measurement equation and the system state equation is as follows:
Figure DEST_PATH_IMAGE091
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE092
is a variance covariance matrix of the state vector;
Figure DEST_PATH_IMAGE093
is a Kalman gain matrix;
Figure 144235DEST_PATH_IMAGE031
a variance covariance matrix for the observation vector;
Figure DEST_PATH_IMAGE094
is a unit array.
An electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor is enabled to implement the GNSS multi-antenna and INS tightly combined positioning and attitude determination method in any of the above technical solutions.
Advantageous effects
The traditional GNSS/INS positioning and attitude determination method firstly solves a baseline vector between a master antenna and a slave antenna, utilizes the baseline vector to solve a carrier attitude, and accordingly establishes a measurement equation of a combination of multiple GNSS antennas and an INS. The method avoids the problem, effectively utilizes the geometrical configuration information and the redundant observation information of the multiple antennas by the tight combination of the observation value level, and can greatly improve the precision and the reliability of the positioning and attitude determination result of the integrated system.
Drawings
Fig. 1 is a general framework diagram of a positioning and attitude determination method using tight combination of GNSS multiple antennas and INS according to an embodiment of the present invention.
Detailed Description
The following describes embodiments of the present invention in detail, which are developed based on the technical solutions of the present invention, and give detailed implementation manners and specific operation procedures to further explain the technical solutions of the present invention.
The embodiment provides a GNSS multi-antenna and INS tightly combined positioning and attitude determination method, which comprises the following steps:
step 1, normalizing coordinate parameters of a plurality of GNSS antennas to inertial navigation center coordinate parameters through a lever arm vector and a rotation matrix, and constructing a double-difference carrier and double-difference pseudo-range rate measurement equation represented by a position vector and a speed vector at an inertial navigation center.
(1) The attitude matrix is initialized. Considering the short baseline and the fixed precision limit of the ambiguity, initializing the INS by adopting the position and the speed of the GNSS antenna, wherein the INS comprises the position, the speed and the posture of an inertial navigation center, and the posture comprises a pitch angle, a roll angle and a course angle; and the attitude is initialized without GNSS fixation solution by adopting an INS self-alignment mode, the pitch angle and the roll angle are calculated by utilizing acceleration leveling, and the heading angle is calculated by utilizing a gyro compass.
(2) Respectively establishing the relationship between the position vector and the velocity vector of each antenna and the position vector and the velocity vector at the inertial navigation center through the lever arm vector and the attitude matrix:
Figure DEST_PATH_IMAGE095
wherein, the first and the second end of the pipe are connected with each other,
Figure 113328DEST_PATH_IMAGE002
、
Figure 533945DEST_PATH_IMAGE003
respectively representing antennas
Figure 272094DEST_PATH_IMAGE004
The position vector and the velocity vector of (c),
Figure 903320DEST_PATH_IMAGE005
、vrespectively representing a position vector and a velocity vector of an inertial navigation center;
Figure 828550DEST_PATH_IMAGE006
is a direction cosine matrix, i.e. a rotation matrix;
Figure 318438DEST_PATH_IMAGE007
is an antenna
Figure 645514DEST_PATH_IMAGE004
A lever arm vector of (a);
Figure 929865DEST_PATH_IMAGE008
is the three-dimensional angular velocity of the IMU output
Figure 607971DEST_PATH_IMAGE009
Of antisymmetric matrices, i.e.
Figure 167128DEST_PATH_IMAGE010
，
Figure 614290DEST_PATH_IMAGE011
Is an antisymmetric array operator;
Figure 69542DEST_PATH_IMAGE012
is an antisymmetric matrix of the rotational angular velocities of the earth.
(3) For antenna
Figure 969365DEST_PATH_IMAGE004
And an antenna
Figure DEST_PATH_IMAGE096
The formed short base line, the ionosphere delay and the troposphere delay between the two antennas have stronger spatial correlation, and the double difference carrier equation and the pseudo range rate equation are approximated as follows:
Figure DEST_PATH_IMAGE097
wherein the content of the first and second substances,
Figure 82945DEST_PATH_IMAGE014
is an antenna
Figure 384614DEST_PATH_IMAGE004
A single difference sight line vector matrix between the satellites, which is
Figure 10767DEST_PATH_IMAGE015
A matrix of dimensions is formed by a matrix of dimensions,
Figure 663465DEST_PATH_IMAGE016
subtracting the number of the adopted satellite systems from the total number of the observation satellites;
Figure DEST_PATH_IMAGE098
is a non-zero diagonal array of corresponding carrier wavelengths,
Figure 298846DEST_PATH_IMAGE019
antenna for representation
Figure 455021DEST_PATH_IMAGE020
Double differences between them observe noise. In addition, in the subscripts
Figure 517655DEST_PATH_IMAGE020
In addition to distinguishing between the different antennas that make up the primary and secondary antennas, it is also used to distinguish between the secondary antenna and the reference station. Namely: when i represents a main antenna, j represents a reference station; when i represents a secondary antenna, j represents a primary antenna;
Figure 126491DEST_PATH_IMAGE046
denotes a subscript
Figure 814830DEST_PATH_IMAGE047
A double-difference carrier observation between them,
Figure 91090DEST_PATH_IMAGE048
denotes a subscript
Figure 59046DEST_PATH_IMAGE047
Double-difference pseudorange rate observations between;
(4) replacing the position vector and the velocity vector of each antenna in the double-difference observation value by using the position vector and the velocity vector at the inertial navigation center to obtain a double-difference carrier wave and double-difference pseudorange rate equation represented by the position vector and the velocity vector at the inertial navigation center:
Figure DEST_PATH_IMAGE099
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE100
。
and 2, considering the correlation when the multi-antenna GNSS observation values form the double-difference observation values, and constructing a multi-antenna observation covariance matrix by using an error propagation law.
Considering the correlation when multi-antenna GNSS observations are combined into dual-difference observations, their covariance matrix can be derived from the error propagation law, so as tonAn antenna andmthe station-to-satellite double-difference observed values formed by the satellites are taken as examples:
Figure DEST_PATH_IMAGE101
wherein, the first and the second end of the pipe are connected with each other,
Figure 951916DEST_PATH_IMAGE058
antenna for representation
Figure 929099DEST_PATH_IMAGE020
And satellite
Figure 59866DEST_PATH_IMAGE057
,
Figure 198724DEST_PATH_IMAGE045
A double-difference observation value between the two,
Figure 47731DEST_PATH_IMAGE059
antenna for representation
Figure 313758DEST_PATH_IMAGE004
To satellite
Figure 564611DEST_PATH_IMAGE057
Is determined from the original observation of the object,
Figure 874370DEST_PATH_IMAGE061
is a transformation matrix between the original non-differential observation and the double-differential observation,
Figure 210673DEST_PATH_IMAGE061
the specific expression of (A) is as follows:
Figure DEST_PATH_IMAGE102
wherein the content of the first and second substances,
Figure 529659DEST_PATH_IMAGE063
to represent
Figure 635018DEST_PATH_IMAGE064
A zero matrix of the dimensions is formed,
Figure DEST_PATH_IMAGE103
the specific expression of (A) is as follows:
Figure DEST_PATH_IMAGE104
then the covariance matrix of the observations of the GNSS multiantenna and INS tightly combined system is:
Figure DEST_PATH_IMAGE105
wherein
Figure 912416DEST_PATH_IMAGE067
The covariance matrix of the original non-difference observation value is a diagonal matrix, and the diagonal element value can be determined according to the carrier-to-noise ratio or the satellite altitude and the like.
And 3, constructing and obtaining a variable correction-based measurement equation of the GNSS multi-antenna and INS tight combination system according to the double-difference carrier wave and double-difference pseudo-range rate measurement equation obtained in the step 1 and the multi-antenna observation covariance matrix obtained in the step 2.
Let the measurement equation of the GNSS multi-antenna and INS tightly combined system be:
Figure 204857DEST_PATH_IMAGE023
wherein the content of the first and second substances,
Figure 573872DEST_PATH_IMAGE024
represents the number of corrections of the variable;
Figure 533737DEST_PATH_IMAGE025
an observation vector representing the combined system, including the carrier and pseudorange rates observed by the GNSS system,
Figure 450878DEST_PATH_IMAGE026
representing GNSS observation vectors
Figure 496194DEST_PATH_IMAGE025
The correction number of the inertial navigation system is obtained by subtracting the carrier wave and the pseudo-range rate of the GNSS and the carrier wave and the pseudo-range rate calculated by the inertial navigation;
Figure 156983DEST_PATH_IMAGE027
representing state vectors
Figure 971355DEST_PATH_IMAGE028
Correcting;
Figure 324976DEST_PATH_IMAGE029
representing a matrix of associations between the two;
Figure 592009DEST_PATH_IMAGE030
representing white noise;
Figure 56489DEST_PATH_IMAGE031
a covariance matrix representing observations of the GNSS multi-antenna and INS tightly combined system.
State vector
Figure 725367DEST_PATH_IMAGE028
Comprises the following steps:
Figure DEST_PATH_IMAGE106
wherein the content of the first and second substances,
Figure 622DEST_PATH_IMAGE005
determining a carrier three-dimensional position vector as an inertial navigation reference center;
Figure 20531DEST_PATH_IMAGE033
representing a velocity vector;
Figure 757542DEST_PATH_IMAGE034
representing a pose vector;
Figure 546507DEST_PATH_IMAGE035
represents the accelerometer zero offset;
Figure 241930DEST_PATH_IMAGE036
represents a gyro zero offset;
Figure 483556DEST_PATH_IMAGE037
representing an accelerometer scale factor;
Figure 24259DEST_PATH_IMAGE038
represents a gyro scale factor;
Figure 933309DEST_PATH_IMAGE039
representing a double difference ambiguity vector.
Due to the fact that
Figure DEST_PATH_IMAGE107
Wherein the content of the first and second substances,
Figure 799634DEST_PATH_IMAGE024
the number of changes of the variable is represented,
Figure 528555DEST_PATH_IMAGE034
representing an attitude vector, writing the double-difference carrier wave and the double-difference pseudorange rate equation obtained in the step 1 into a measurement equation form, and obtaining a relation matrix between the observation vector correction and the state vector correction as follows:
Figure DEST_PATH_IMAGE108
wherein, the first and the second end of the pipe are connected with each other,
Figure DEST_PATH_IMAGE109
to represent
Figure 387796DEST_PATH_IMAGE053
The zero matrix of the dimension(s) is,
Figure DEST_PATH_IMAGE110
is a non-zero diagonal array of corresponding carrier wavelengths,
Figure DEST_PATH_IMAGE111
is specifically expressed as follows:
Figure 416932DEST_PATH_IMAGE056
make up the whole GNSS for a plurality of daysWhen a measurement equation of a line and INS tight combination system is used, one mobile antenna is usually selected as a main antenna, the other mobile antennas are used as auxiliary antennas, the main antenna and a reference station form a double-difference observation equation to provide a position reference for the whole combination system, and meanwhile, the double-difference observation equation is formed between the main antenna and the auxiliary antennas to fully utilize a multi-antenna redundancy observation value. With p mobile antennas (subscript of main antenna)
Figure DEST_PATH_IMAGE112
The auxiliary antenna subscripts are respectively
Figure DEST_PATH_IMAGE113
) And q reference stations (subscripts are respectively
Figure DEST_PATH_IMAGE114
) For example, the observation vector is corrected
Figure 719737DEST_PATH_IMAGE026
Comprises the following steps:
Figure DEST_PATH_IMAGE115
wherein each element represents a correction to a double-difference observation vector between antennas with subscripts, e.g.
Figure DEST_PATH_IMAGE116
Indicating a main antenna
Figure 217845DEST_PATH_IMAGE112
And a reference station
Figure DEST_PATH_IMAGE117
The double difference carrier between them observes the vector correction.
Its relation matrix
Figure 365930DEST_PATH_IMAGE029
Comprises the following steps:
Figure DEST_PATH_IMAGE118
wherein, each element represents a link matrix between the double-difference observation vector correction number and the state vector correction number between the antennas corresponding to the subscript.
And 4, establishing a system state equation by using the position, the speed, the attitude, the sensor zero offset and the error of the scale factor at the inertial navigation center as a state vector of the system and adopting a first-order Gaussian Markov process.
The state equation of the system established by adopting the first-order Gaussian Markov process is as follows:
Figure 249572DEST_PATH_IMAGE069
wherein
Figure 192121DEST_PATH_IMAGE070
Is a state vector
Figure 895634DEST_PATH_IMAGE028
At the moment of time
Figure 581831DEST_PATH_IMAGE071
The superscript "-" indicates that a variable has not been updated by the most recent observation, and once updated, the corresponding superscript will become "+";
Figure 54400DEST_PATH_IMAGE072
in order to be a state transition matrix,
Figure 167850DEST_PATH_IMAGE073
for the process noise vector, assuming a normal distribution obeying zero mean,
Figure 358660DEST_PATH_IMAGE074
is a transfer matrix for the process noise,
Figure 582968DEST_PATH_IMAGE075
a covariance matrix that is the process noise;
Figure 427820DEST_PATH_IMAGE072
the specific expression of (A) is as follows:
Figure DEST_PATH_IMAGE119
Figure 243330DEST_PATH_IMAGE077
Figure 655856DEST_PATH_IMAGE078
wherein, the first and the second end of the pipe are connected with each other,
Figure 683855DEST_PATH_IMAGE005
the three-dimensional position vector of the inertial navigation center is obtained;
Figure 131017DEST_PATH_IMAGE079
the distance between the earth surface and the earth center;
Figure 586269DEST_PATH_IMAGE080
is a gravity vector;
Figure 751671DEST_PATH_IMAGE081
is the three-dimensional specific force vector output by the accelerometer;
Figure 583361DEST_PATH_IMAGE009
a three-dimensional angular velocity output for the IMU;
Figure DEST_PATH_IMAGE120
to be composed of
Figure 885029DEST_PATH_IMAGE009
A diagonal matrix being diagonal elements;
Figure DEST_PATH_IMAGE121
the correlation time can be obtained by Allan variance analysis;
Figure 527495DEST_PATH_IMAGE089
time intervals are measured for the accelerometer and gyroscope.
And 5, performing Kalman filtering solution on the measurement equation and the system state equation to obtain the optimal estimation of the position, the speed and the attitude of the inertial navigation center at each moment.
The Kalman filtering concrete recursion calculation formula is as follows:
Figure 180193DEST_PATH_IMAGE091
wherein the content of the first and second substances,
Figure 549994DEST_PATH_IMAGE070
is a state vector
Figure 971748DEST_PATH_IMAGE028
At the moment of time
Figure 34382DEST_PATH_IMAGE071
The superscript "-" indicates that a variable has not been updated by the most recent observation, and once updated, the corresponding superscript will become "+";
Figure 643218DEST_PATH_IMAGE072
in order to be a state transition matrix,
Figure 82290DEST_PATH_IMAGE073
for the process noise vector, assuming a normal distribution obeying zero mean,
Figure 358550DEST_PATH_IMAGE074
is a transfer matrix for the process noise,
Figure DEST_PATH_IMAGE122
a covariance matrix that is the process noise;
Figure 592085DEST_PATH_IMAGE092
is a variance covariance matrix of the state vector;
Figure 203064DEST_PATH_IMAGE093
is a Kalman gain matrix;
Figure 649089DEST_PATH_IMAGE031
a variance covariance matrix for the observation vector;
Figure 45435DEST_PATH_IMAGE094
is a unit array.
The attitude determination and positioning method using the tight combination of the GNSS multi-antenna and the INS is shown by referring to FIG. 1, and the complete process is as follows:
(1) and processing the original observed values of the multiple antennas, selecting one mobile antenna as a main antenna, using the other mobile antennas as auxiliary antennas, forming a double-difference observation equation between the main antenna and the reference station, forming the double-difference observation equation between the main antenna and the auxiliary antennas, and performing relative positioning calculation to obtain the position, speed and attitude information of the combined system.
(2) And performing initial alignment on the IMU by using the information, when no GNSS fixed solution exists, initializing the attitude by adopting an INS self-alignment mode, leveling by using acceleration to calculate a pitch angle and a roll angle, and calculating a heading angle by using a gyro compass.
(3) And updating the position, speed and attitude information of the combined system according to the output of the IMU, firstly, finishing attitude updating by utilizing the angular rate output by the gyroscope, carrying out coordinate conversion on the specific force output by the accelerometer on the basis, and finally updating the speed and position information.
(4) And forming a state equation and a measurement equation of Kalman filtering, calculating a carrier wave and pseudo-range rate observation value according to the updated position, speed and attitude information and satellite ephemeris, taking the difference between the carrier wave and pseudo-range rate observed by a GNSS system as the correction number of an observation vector in the measurement equation, respectively establishing the relationship between a position vector and a speed vector of each antenna and a position vector and a speed vector at an inertial navigation center through a lever arm vector and an attitude matrix, replacing the position vector and the speed vector of each antenna in the measurement equation by the position vector and the speed vector at the inertial navigation center, taking errors such as the position, the speed, the attitude, the sensor zero offset and the like at the inertial navigation center as the state vector of the system, and simultaneously establishing the state equation of the system by adopting a first-order Gaussian Markov process.
(5) And performing Kalman filtering solution to obtain optimal estimation of the position, the speed and the attitude of the inertial navigation center at each moment, and performing feedback correction on the sensor error.
In conclusion, the new method for tightly combining the GNSS multi-antenna and the INS to position and fix the attitude utilizes the geometric configuration information and the redundant observation information of the multi-antenna, relieves the problem that a single-antenna GNSS is poor in satellite visibility and signal anti-interference capability in a severe environment, improves the fault tolerance of the system, fully utilizes observation data compared with the traditional GNSS/INS positioning and attitude fixing method based on the ambiguity fixed base line, and is beneficial to improving the stability and the accuracy of an integrated system.
The above embodiments are preferred embodiments of the present application, and those skilled in the art can make various changes or modifications without departing from the general concept of the present application, and such changes or modifications should fall within the scope of the claims of the present application.

Claims (10)

1. A GNSS multi-antenna and INS tightly combined positioning and attitude determination method is characterized by comprising the following steps:
step 1, normalizing coordinate parameters of a plurality of GNSS antennas to inertial navigation center coordinate parameters through a lever arm vector and a rotation matrix, and constructing a double-difference carrier and double-difference pseudo-range rate measurement equation represented by a position vector and a speed vector at an inertial navigation center;
step 2, considering the correlation when the multi-antenna GNSS observation values form a double-difference observation value, and constructing a covariance matrix of the observation values of the GNSS multi-antenna and INS tight combination system by using an error propagation law;
step 3, according to the double difference carrier wave and double difference pseudo range rate measurement equation obtained in the step 1 and the multi-antenna observation covariance matrix obtained in the step 2, a variable correction-based measurement equation of the GNSS multi-antenna and INS tight combination system is constructed;
step 4, taking the position, the speed, the attitude, the zero offset of the sensor and the error of the scale factor at the inertial navigation center as the state vector of the system, and establishing a system state equation by adopting a first-order Gaussian Markov process;
and 5, performing Kalman filtering solution according to the measurement equation and the system state equation to obtain the optimal estimation of the position, the speed and the attitude of the inertial navigation center at each moment.
2. The method for positioning and determining the attitude according to claim 1, wherein the method for normalizing the coordinate parameters of the GNSS antenna to the inertial navigation center coordinate parameters comprises:
Figure 654149DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 894637DEST_PATH_IMAGE002
、
Figure 845275DEST_PATH_IMAGE003
respectively represent an antenna
Figure 960737DEST_PATH_IMAGE004
The position vector and the velocity vector of (c),
Figure 47641DEST_PATH_IMAGE005
、
Figure 724610DEST_PATH_IMAGE006
respectively representing a position vector and a velocity vector of an inertial navigation center;
Figure 896966DEST_PATH_IMAGE007
is a direction cosine matrix, i.e. a rotation matrix;
Figure 317583DEST_PATH_IMAGE008
is an antenna
Figure 524573DEST_PATH_IMAGE004
The lever arm vector of (a);
Figure 372444DEST_PATH_IMAGE009
is the three-dimensional angular velocity of the IMU output
Figure 32095DEST_PATH_IMAGE010
Of antisymmetric matrices, i.e.
Figure 256403DEST_PATH_IMAGE011
，
Figure 317900DEST_PATH_IMAGE012
Is an antisymmetric array operator;
Figure 336671DEST_PATH_IMAGE013
is an antisymmetric matrix of the rotational angular velocity of the earth.
3. A method for positioning and attitude determination according to claim 2, characterized by constructing double-differenced carrier and double-differenced pseudorange rate equations expressed in a position vector and a velocity vector at the inertial navigation center, expressed as:
Figure 483619DEST_PATH_IMAGE014
wherein the content of the first and second substances,
Figure 246039DEST_PATH_IMAGE015
is an antenna
Figure 162042DEST_PATH_IMAGE004
A single difference sight line vector matrix between the satellites, which is
Figure 617294DEST_PATH_IMAGE016
A matrix of dimensions is formed by a matrix of dimensions,
Figure 251538DEST_PATH_IMAGE017
subtracting the number of adopted satellite systems from the total number of the observation satellites;
Figure 552069DEST_PATH_IMAGE018
the amount of the carbon dioxide is the intermediate amount,
Figure 322579DEST_PATH_IMAGE019
is a non-zero diagonal matrix of corresponding carrier wavelengths,
Figure 948732DEST_PATH_IMAGE020
antenna for representation
Figure 804693DEST_PATH_IMAGE021
Double difference observation noise between the two;
Figure 174495DEST_PATH_IMAGE022
antenna for representation
Figure 65090DEST_PATH_IMAGE021
The two-difference carrier observations in between,
Figure 596566DEST_PATH_IMAGE023
antenna for representation
Figure 205401DEST_PATH_IMAGE021
Double-differenced pseudorange rate observations between.
4. The method according to claim 1, wherein the measurement equation obtained in step 3 is expressed as:
Figure 346271DEST_PATH_IMAGE024
wherein, the first and the second end of the pipe are connected with each other,
Figure 91373DEST_PATH_IMAGE025
a correction number representing a variable;
Figure 59329DEST_PATH_IMAGE026
the observation vector representing the GNSS antenna combined system comprises the carrier wave and the pseudo range rate observed by the GNSS system,
Figure 889881DEST_PATH_IMAGE027
representing observation vectors
Figure 335906DEST_PATH_IMAGE026
The correction number of the inertial navigation system is obtained by subtracting the carrier wave and the pseudo-range rate of the GNSS and the carrier wave and the pseudo-range rate calculated by the inertial navigation system;
Figure 466673DEST_PATH_IMAGE028
representing state vectors
Figure DEST_PATH_IMAGE029
Correcting;
Figure 74372DEST_PATH_IMAGE030
indicating the number of corrections of the observation vector
Figure 392221DEST_PATH_IMAGE027
And state vector correction number
Figure 641937DEST_PATH_IMAGE031
A matrix of relationships between;
Figure 361631DEST_PATH_IMAGE032
representing white noise;
Figure 671390DEST_PATH_IMAGE033
a covariance matrix representing the observations;
state vector
Figure 210955DEST_PATH_IMAGE029
Comprises the following steps:
Figure 998783DEST_PATH_IMAGE034
wherein the content of the first and second substances,
Figure 838563DEST_PATH_IMAGE005
determining a carrier three-dimensional position vector as an inertial navigation reference center;
Figure 53644DEST_PATH_IMAGE035
representing a velocity vector;
Figure 346085DEST_PATH_IMAGE036
representing a pose vector;
Figure 937603DEST_PATH_IMAGE037
represents the accelerometer zero offset;
Figure 631890DEST_PATH_IMAGE038
represents a gyro zero bias;
Figure 283451DEST_PATH_IMAGE039
representing an accelerometer scale factor;
Figure 797609DEST_PATH_IMAGE040
represents a gyro scale factor;
Figure 927239DEST_PATH_IMAGE041
representing a double-difference ambiguity vector.
5. The method according to claim 4, wherein the number of correction of the observation vector is set to be equal to or less than the number of correction of the observation vector
Figure 741611DEST_PATH_IMAGE042
And a matrix of associations
Figure 298494DEST_PATH_IMAGE043
Respectively as follows:
Figure 821921DEST_PATH_IMAGE044
wherein the content of the first and second substances,
Figure 755242DEST_PATH_IMAGE045
a main antenna is shown, which is,
Figure DEST_PATH_IMAGE046
to represent
Figure 158541DEST_PATH_IMAGE047
A plurality of auxiliary antennas are arranged on the base plate,
Figure 151905DEST_PATH_IMAGE048
represent
Figure 640655DEST_PATH_IMAGE049
A reference station;
Figure 377667DEST_PATH_IMAGE050
denotes a subscript
Figure 901052DEST_PATH_IMAGE051
A double-difference carrier observation between them,
Figure 799738DEST_PATH_IMAGE052
denotes a subscript
Figure 775785DEST_PATH_IMAGE051
Double-difference pseudorange rate observations between;
Figure DEST_PATH_IMAGE053
represent a subscript
Figure 50908DEST_PATH_IMAGE051
A matrix of associations between the associated double difference vector corrections and the state vector corrections, and having:
Figure 163221DEST_PATH_IMAGE054
wherein, the first and the second end of the pipe are connected with each other,
Figure 498387DEST_PATH_IMAGE055
to represent
Figure DEST_PATH_IMAGE056
The zero matrix of the dimension(s) is,
Figure 696150DEST_PATH_IMAGE057
for non-zero diagonal arrays of corresponding carrier wavelengths, intermediate variables
Figure 40544DEST_PATH_IMAGE058
The specific expression of (A) is as follows:
Figure 7363DEST_PATH_IMAGE059
。
6. the method according to claim 4, wherein the covariance matrix of observations of the GNSS multi-antenna and INS tightly-combined system is constructed using the law of error propagation
Figure 513430DEST_PATH_IMAGE060
The method comprises the following steps:
first, the antenna is mounted
Figure 198490DEST_PATH_IMAGE021
And satellite
Figure 80995DEST_PATH_IMAGE061
,
Figure 167900DEST_PATH_IMAGE049
The double difference between the observed values is expressed as
Figure 844869DEST_PATH_IMAGE062
Will be arbitrary antenna
Figure 282803DEST_PATH_IMAGE004
For any satellite
Figure 201956DEST_PATH_IMAGE061
Is expressed as
Figure 408946DEST_PATH_IMAGE063
Then the original non-differential observed value can be obtained from the law of error propagation
Figure 256816DEST_PATH_IMAGE063
And double difference observed value
Figure 916468DEST_PATH_IMAGE062
The relationship between them is:
Figure 140776DEST_PATH_IMAGE064
then, the conversion matrix is calculated according to the relational expression
Figure 202273DEST_PATH_IMAGE065
Comprises the following steps:
Figure 955465DEST_PATH_IMAGE066
wherein the content of the first and second substances,
Figure 367992DEST_PATH_IMAGE067
represent
Figure 130411DEST_PATH_IMAGE068
A zero matrix of the dimensions is formed,
Figure 46415DEST_PATH_IMAGE069
the specific expression of (A) is as follows:
Figure 501667DEST_PATH_IMAGE070
finally, according to the transformation matrix
Figure 870331DEST_PATH_IMAGE065
And covariance matrix of original non-differential observations
Figure 170863DEST_PATH_IMAGE071
Determining the covariance matrix of the combined system observations as:
Figure 472531DEST_PATH_IMAGE072
。
7. the method according to claim 4, wherein the correction of the observation vector is performed by using a correction value of the observation vector
Figure 833105DEST_PATH_IMAGE042
The calculation method comprises the following steps: calculating a double-difference carrier observation value and a double-difference pseudo range rate observation value according to position, speed and attitude information updated by an inertial navigation center and a satellite ephemeris; and (4) subtracting the carrier wave and the pseudo-range rate obtained by the observation of the GNSS system, and using the difference as the correction number of the observation vector in the measurement equation.
8. The method according to claim 7, wherein a double-difference observation equation is constructed from the observed values of the multi-antenna GNSS system, and the position, velocity and attitude information of the combined system is obtained by solving the double-difference observation equation and is used for initializing the inertial navigation center.
9. The method according to claim 4, wherein the state equation of the system is established by a first-order Gaussian Markov process as follows:
Figure 689066DEST_PATH_IMAGE073
wherein the content of the first and second substances,
Figure 58867DEST_PATH_IMAGE074
is a state vector
Figure 949463DEST_PATH_IMAGE029
At the moment of time
Figure 480938DEST_PATH_IMAGE075
The superscript "-" indicates that a variable has not been updated by the most recent observation, and once updated, the corresponding superscript will become "+";
Figure 89774DEST_PATH_IMAGE076
in order to be a state transition matrix,
Figure 732108DEST_PATH_IMAGE077
for the process noise vector, assuming a normal distribution following zero mean,
Figure 477210DEST_PATH_IMAGE078
is a transfer matrix for the process noise,
Figure 445166DEST_PATH_IMAGE079
a covariance matrix that is the process noise;
Figure 275719DEST_PATH_IMAGE076
the specific expression of (A) is as follows:
Figure 987323DEST_PATH_IMAGE080
Figure 85467DEST_PATH_IMAGE081
Figure 958745DEST_PATH_IMAGE082
wherein the state transition matrix
Figure 276594DEST_PATH_IMAGE076
The 3 in each element subscript in (a) represents a 3 x 3 matrix,nto representn×n3 is generatednRepresents 3 linesnA matrix of the columns is formed,nx 3 representsnA matrix of rows and 3 columns;
Figure 791889DEST_PATH_IMAGE005
the three-dimensional position vector of the inertial navigation center is obtained;
Figure 246004DEST_PATH_IMAGE083
the distance between the earth surface and the earth center;
Figure 290183DEST_PATH_IMAGE084
is a gravity vector;
Figure 360907DEST_PATH_IMAGE085
is the three-dimensional specific force vector output by the accelerometer;
Figure 148735DEST_PATH_IMAGE010
a three-dimensional angular velocity output for the IMU;
Figure 722936DEST_PATH_IMAGE086
to be composed of
Figure 203596DEST_PATH_IMAGE010
A diagonal matrix being diagonal elements;
Figure 496037DEST_PATH_IMAGE087
are all intermediate variables;
Figure 87555DEST_PATH_IMAGE088
for the correlation time of the accelerometer zero-offset,
Figure 516262DEST_PATH_IMAGE089
is the relative time of the gyro zero offset,
Figure 167823DEST_PATH_IMAGE090
is the correlation time of the accelerometer scale factor,
Figure 947561DEST_PATH_IMAGE091
the correlation time of the gyro scale factor;
Figure 77191DEST_PATH_IMAGE092
measuring time intervals for the accelerometer and gyroscope;
Figure 625984DEST_PATH_IMAGE093
is an antisymmetric matrix of the rotational angular velocity of the earth;
the specific recursion calculation formula for performing Kalman filtering solution according to the measurement equation and the system state equation is as follows:
Figure 182867DEST_PATH_IMAGE094
wherein the content of the first and second substances,
Figure 449900DEST_PATH_IMAGE095
is a state directionVariance covariance matrix of the quantities;
Figure 383221DEST_PATH_IMAGE096
is a Kalman gain matrix;
Figure 52100DEST_PATH_IMAGE060
a variance covariance matrix for the observation vector;
Figure 779884DEST_PATH_IMAGE097
is a unit array.
10. An electronic device comprising a memory and a processor, the memory having stored therein a computer program, wherein the computer program, when executed by the processor, causes the processor to implement the method of any of claims 1-9.
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