CN115790652A - Odometer/dual-antenna GNSS space online calibration method - Google Patents

Odometer/dual-antenna GNSS space online calibration method Download PDF

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CN115790652A
CN115790652A CN202211466306.7A CN202211466306A CN115790652A CN 115790652 A CN115790652 A CN 115790652A CN 202211466306 A CN202211466306 A CN 202211466306A CN 115790652 A CN115790652 A CN 115790652A
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odometer
attitude
initial
time
carrier
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徐晓苏
仲灵通
姚逸卿
高佳誉
何宇明
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Southeast University
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Southeast University
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Abstract

The invention discloses a speedometer/double-antenna GNSS space online calibration method, which comprises the following steps: firstly, selecting an initial attitude error and a lever arm as state quantities, establishing a Kalman filtering state equation and discretizing; then, the difference value of the relative position of the odometer at the same moment and the position of the double-antenna GNSS after coordinate transformation is used as Kalman filtering observed quantity to establish a Kalman filtering measurement equation; then Kalman filtering is carried out to obtain initial attitude error estimation and lever arm estimation; then, correcting the initial attitude by using the initial attitude error estimation feedback and setting the initial attitude error estimation to be zero; then, carrying out attitude alignment on the relative attitude of the odometer by utilizing the initial attitude to obtain an absolute attitude; then calculating by using the absolute course of the double-antenna GNSS and the absolute attitude of the odometer at the same time to obtain the installation deflection angle of the double-antenna GNSS and the odometer; the last 5 steps are repeated until the initial attitude and the lever arm converge to their respective exact quantities. The invention can accurately, quickly and conveniently realize the on-line calibration of the odometer and the double-antenna GNSS space.

Description

Odometer/dual-antenna GNSS space online calibration method
Technical Field
The invention relates to a odometer/dual-antenna GNSS space online calibration method, belongs to the sensor space synchronization technology, and is particularly suitable for the field of navigation positioning.
Background
With the rapid development of relative positioning and orientation odometers such as laser radar odometers and visual odometers and the like and the hot demand of multi-source information fusion perception and positioning in the automatic driving field, the method has great significance for solving the fusion problem of relative positioning and orientation information and absolute positioning and orientation information. Global Navigation Satellite Systems (GNSS) are currently the dominant absolute positioning system, and dual-antenna GNSS can also provide absolute orientation information. In order to realize information fusion between a laser radar odometer, a visual odometer and the like relative odometer and a GNSS, positioning and orientation information of the laser radar odometer, the visual odometer and the like needs to be converted into the same reference coordinate system, but the reference coordinate system (such as an initial front-left uploading system) of the relative odometer is usually inconsistent with the reference coordinate system (such as a northeast geographic system) of the GNSS relative positioning, an unfixed course deviation exists, and a lever arm error also exists. In addition, in order to ensure the directional accuracy of the dual-antenna GNSS, the length of the base line of the master and slave antennas needs to be extended as much as possible, the master and slave antennas are often installed diagonally, so that an included angle exists between the master and slave antennas and the central axis of the carrier, and the laser radar, the camera and the like are often installed along the central axis of the carrier, so that the installation declination calibration of the master and slave antennas is required before the dual-antenna GNSS directional information is used. The sensor error calibration is divided into an online mode and an offline mode. The online calibration has the characteristics of flexibility, convenience and quickness, and has practical application value. Kalman filtering is a commonly used online calibration algorithm and has the characteristics of simple algorithm and small calculated amount. Currently, the work of space calibration of a speedometer and a dual-antenna GNSS is rarely reported, and therefore, a more effective and rapid space online calibration method is urgently needed for the above situations.
Disclosure of Invention
In order to meet the application requirements of accurate, rapid and convenient space online calibration of a relative positioning and orientation odometer (such as a laser radar odometer, a visual odometer, a dead reckoning odometer and the like) and a dual-antenna GNSS, the invention provides an odometer/dual-antenna GNSS space online calibration method.
The above purpose of the invention is realized by the following technical scheme:
a odometer/double-antenna GNSS space online calibration method specifically comprises the following steps:
step S1: selecting an initial attitude error and a lever arm as state quantities, establishing a Kalman filtering state equation and discretizing;
step S2: converting the geographic coordinate of the GNSS measuring carrier into a geocentric rectangular coordinate;
and step S3: taking the difference value of the relative position of the odometer at the same moment and the position of the double-antenna GNSS after coordinate transformation as the observed quantity of Kalman filtering, and establishing a Kalman filtering measurement equation;
and step S4: performing Kalman filtering to obtain initial attitude error estimation and lever arm estimation;
step S5: correcting the initial attitude by using the initial attitude error estimation feedback and setting the initial attitude error estimation to be zero;
step S6: carrying out attitude alignment on the relative attitude of the odometer by utilizing the initial attitude to obtain an absolute attitude;
step S7: calculating the installation deflection angle of the double-antenna GNSS and the odometer by using the absolute attitude of the odometer after the absolute course and the attitude of the double-antenna GNSS at the same moment are aligned;
step S8: and repeating the steps S2 to S7 until the initial posture and the lever arm converge to respective accurate quantities.
Further, the step S1 specifically includes the following steps:
s1.1, selecting an initial attitude error and a lever arm as state quantities, and establishing a Kalman filtering state equation:
Figure BDA0003957658410000021
wherein, X is a state vector,
Figure BDA0003957658410000022
delta phi is the initial attitude error vector, delta phi = [0 delta phi = u ] Τ ，δφ u The error of the heading deflection angle is shown,l is vector tie rod arm vector, l = [ l = x l y 0] Τ ，l x And l y The vector is the x-axis and y-axis shaft lever arm vector of the carrier system respectively; f is a system matrix, F =0 6×6 (ii) a W is the systematic noise vector, W =0 6×1 ；
S1.2 discretizes the equation of state:
X(k)＝Φ(k,k-1)X(k-1)
wherein X (k) is a state vector at the time of k; phi (k, k-1) is a state one-step transition matrix from k-1 time to k time, and phi (k, k-1) = I 4×4 。
Further, the step S2 specifically includes the following steps:
measuring geographical coordinates of a carrier using GNSS
Figure BDA0003957658410000023
Converting to geocentric rectangular coordinates
Figure BDA0003957658410000024
Figure BDA0003957658410000025
Wherein, λ (k), L (k), h (k) are respectively longitude, latitude, altitude, R of GNSS measurement carrier at the moment of k N Is the curvature radius of the unitary-mortise ring,
Figure BDA0003957658410000026
e is the eccentricity of the earth
Figure BDA0003957658410000027
R e And R p Respectively a long half shaft and a short half shaft of the earth.
Further, the step S3 specifically includes the following steps:
s3.1, taking the difference value of the relative position of the odometer at the same moment and the position of the dual-antenna GNSS after coordinate transformation as the observed quantity of Kalman filtering:
Figure BDA0003957658410000028
Figure BDA0003957658410000031
Figure BDA0003957658410000032
wherein Z (k) is a measurement vector at the moment k; setting the loading system to coincide with the coordinate system of the odometer;
Figure BDA0003957658410000033
the odometer position vector of the carrier at the moment k relative to the initial moment carrier system b (0);
Figure BDA0003957658410000034
the conversion relation between the initial time carrier system b (0) estimated at the time k-1 and the local horizontal geographic coordinate system n (0) where the initial time carrier is located is represented;
Figure BDA0003957658410000035
the position matrix of the initial time carrier represents the conversion relation between a local horizontal geographic coordinate system n (0) where the initial time carrier is located and a geocentric geostationary rectangular coordinate system e;
Figure BDA0003957658410000036
the vector is a projection of a carrier GNSS position vector at the time k relative to the initial time in a geographical coordinate system n (0) at the initial time;
Figure BDA0003957658410000037
and
Figure BDA0003957658410000038
the geocentric rectangular coordinates of the carrier calculated by the step S2 at the initial time and the k time respectively;
s3.2, establishing a Kalman filtering measurement equation:
Z(k)＝H(k)X(k)+V(k)
Figure BDA0003957658410000039
wherein H (k) is a measurement matrix at the time k; v (k) is a measurement noise vector at the k moment;
Figure BDA00039576584100000310
the attitude matrix output by the odometer represents the conversion relation between the carrier system b (k) at the moment k and the carrier system b (0) at the initial moment;
Figure BDA00039576584100000311
to represent
Figure BDA00039576584100000312
Is used to generate the inverse symmetric matrix.
Further, the step S4 specifically includes the following steps:
s4, kalman filtering is carried out to obtain initial attitude error estimation and lever arm estimation:
Figure BDA00039576584100000313
P(k,k-1)＝Φ(k,k-1)P(k-1)Φ(k,k-1) T
K(k)＝P(k,k-1)H(k) T (H(k)P(k,k-1)H(k) T +R(k)) -1
Figure BDA00039576584100000314
P(k)＝(I-K(k)H(k))P(k,k-1)
wherein the content of the first and second substances,
Figure BDA00039576584100000315
and P (k, k-1) is state one-step prediction and its corresponding mean square error matrix;
Figure BDA00039576584100000316
and P (k) is the state estimation at the time k and the corresponding mean square error matrix; k (K) is a filtering gain array at the K moment; r (k) is a measurement noise variance matrix at the time k.
Further, the step S5 specifically includes the following steps:
s5.1, correcting the initial attitude by using the estimation feedback of the initial attitude error:
Figure BDA0003957658410000041
Figure BDA0003957658410000042
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003957658410000043
estimating initial attitude error for time k
Figure BDA0003957658410000044
Corresponding transformation matrix representing the real initial time carrier system b 0 Initial time carrier system with time k estimation
Figure BDA0003957658410000045
The conversion relationship of (1);
Figure BDA0003957658410000046
the initial attitude matrix at the time k obtained after feedback correction represents a local horizontal geographic coordinate system n (0) where the initial time carrier is positioned and an initial time carrier system estimated at the time k
Figure BDA0003957658410000047
The conversion relationship of (1);
s5.2, zero setting initial attitude error estimation:
Figure BDA0003957658410000048
further, the step S6 specifically includes the following steps:
s6, carrying out attitude alignment on the relative attitude of the odometer by utilizing the initial attitude to obtain an absolute attitude:
Figure BDA0003957658410000049
Figure BDA00039576584100000410
wherein the content of the first and second substances,
Figure BDA00039576584100000411
representing the conversion relation between a k moment carrier system b (k) and a k moment geographic coordinate system n (k) for the k moment odometer absolute attitude matrix after attitude alignment;
Figure BDA00039576584100000412
and the conversion relation between the initial time geographic coordinate system n (0) and the k time geographic coordinate system n (k) is shown.
Further, the step S7 specifically includes the following steps:
s7, calculating by using the absolute course of the double-antenna GNSS at the same time and the absolute attitude of the odometer after the attitude is aligned to obtain the installation deflection angle of the double-antenna GNSS and the carrier:
Figure BDA00039576584100000413
wherein the content of the first and second substances,
Figure BDA00039576584100000414
representing the conversion relation between a carrier system and a GNSS coordinate system for an installation deflection angle matrix of the dual-antenna GNSS and the carrier at the moment k;
Figure BDA00039576584100000415
representing a k-time GNSS coordinate system and geography for a k-time dual-antenna GNSS absolute course matrixAnd (4) conversion relation between coordinate systems.
The invention has the following advantages and beneficial effects:
(1) According to the invention, a Kalman filtering method is adopted, so that lever arms and installation deflection angles of the odometer and the dual-antenna GNSS can be calibrated quickly on line;
(2) The problems that a reference coordinate system of a relative positioning and orientation odometer is inconsistent with a GNSS absolute positioning and orientation reference coordinate system and course deviation is not fixed are solved through on-line attitude alignment;
(3) The invention has no strict restriction on the motion trail of the carrier during calibration, and the calibration can be conveniently completed by selecting a commonly used 8-shaped track;
(4) The odometer provided by the invention is a general odometer capable of calculating and outputting relative position and posture, and is not limited to a laser radar odometer, a visual odometer, a dead reckoning odometer and the like;
(5) The attitude alignment method is also suitable for single-antenna GNSS conditions, and can solve the initial alignment problem of micro inertial base combined navigation.
Drawings
Fig. 1 is a schematic block diagram of a odometer/dual-antenna GNSS space online calibration method according to the present invention.
FIG. 2 is a diagram illustrating a lidar and dual-antenna GNSS mounting layout and coordinate system definition in accordance with an embodiment.
Fig. 3 is a schematic diagram illustrating a relative relationship between the initial time carrier system b (0) and the local horizontal geographic coordinate system n (0) where the initial time carrier is located in the embodiment.
FIG. 4 is a schematic view of LIDAR system and dual-antenna GNSS system installation angling in the illustrated embodiment.
FIG. 5 is a schematic diagram illustrating a comparison between a GNSS trajectory and a lidar odometer trajectory in this embodiment.
Fig. 6 is a graph showing the evaluation results of the lever arm in the embodiment.
Fig. 7 is a heading and drift angle estimation result diagram of the initial time carrier system b (0) and the local horizontal geographic coordinate system n (0) where the initial time carrier is located in the embodiment.
FIG. 8 is a diagram illustrating the results of the LIDAR system and dual-antenna GNSS system setup bias angle calculations in the illustrated embodiment.
Detailed Description
The technical solutions provided by the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments, and it should be understood that the following detailed description is only used for illustrating the present invention and is not used to limit the scope of the present invention.
Example 1: the invention provides a speedometer/double-antenna GNSS space online calibration method, the realization principle is as shown in figure 1, in the specific embodiment of laser radar speedometer/double-antenna GNSS space online calibration, the method specifically comprises the following steps:
step S1: selecting an initial attitude error and a lever arm as state quantities, establishing a Kalman filtering state equation and discretizing:
s1.1, selecting an initial attitude error and a lever arm as state quantities, and establishing a Kalman filtering state equation:
Figure BDA0003957658410000051
wherein, X is a state vector,
Figure BDA0003957658410000052
delta phi is an initial attitude error vector, delta phi = [0 ] u ] Τ ，δφ u Is the heading deflection angle error, l is the carrier tie rod arm vector, l = [ l = x l y 0] Τ ，l x And l y The vector is the x-axis and y-axis shaft lever arm vector of the carrier system respectively; f is a system matrix, F =0 6×6 (ii) a W is the systematic noise vector, W =0 6×1 ；
S1.2 discretizes the equation of state:
X(k)＝Φ(k,k-1)X(k-1)
wherein X (k) is a state vector at the time of k; phi (k, k-1) is a state one-step transition matrix from k-1 time to k time, and phi (k, k-1) = I 4×4 。
Step S2: measuring geographical coordinates of a carrier using GNSS
Figure BDA0003957658410000061
Converting to geocentric rectangular coordinates
Figure BDA0003957658410000062
Figure BDA0003957658410000063
Wherein, λ (k), L (k), h (k) are respectively longitude, latitude, altitude, R of GNSS measurement carrier at the moment of k N The radius of curvature of the prime zone is,
Figure BDA0003957658410000064
e is the eccentricity of the earth
Figure BDA0003957658410000065
R e And R p Respectively a long half shaft and a short half shaft of the earth.
And step S3: taking the difference value of the relative position of the odometer at the same moment and the position of the double-antenna GNSS after coordinate transformation as the observed quantity of Kalman filtering, and establishing a Kalman filtering measurement equation:
s3.1, taking the difference value of the relative position of the odometer at the same moment and the position of the dual-antenna GNSS after coordinate transformation as the observed quantity of Kalman filtering:
Figure BDA0003957658410000066
Figure BDA0003957658410000067
Figure BDA0003957658410000068
wherein Z (k) is a measurement vector at the moment k; setting the loading system to coincide with the coordinate system of the odometer;
Figure BDA0003957658410000069
the odometer position vector of the carrier at the moment k relative to the initial moment carrier system b (0);
Figure BDA00039576584100000610
representing the conversion relation between the initial time carrier system b (0) estimated at the time k-1 and the local horizontal geographic coordinate system n (0) where the initial time carrier is located;
Figure BDA00039576584100000611
the position matrix of the initial time carrier represents the conversion relation between a local horizontal geographic coordinate system n (0) where the initial time carrier is located and a geocentric earth-fixed rectangular coordinate system e;
Figure BDA00039576584100000612
the vector is a projection of a carrier GNSS position vector at the time k relative to the initial time in a geographical coordinate system n (0) at the initial time;
Figure BDA00039576584100000613
and
Figure BDA00039576584100000614
the geocentric rectangular coordinates of the carrier calculated in the step S2 are respectively the initial time and the k time;
s3.2, establishing a Kalman filtering measurement equation:
Z(k)＝H(k)X(k)+V(k)
Figure BDA0003957658410000071
wherein H (k) is a measurement matrix at the time k; v (k) is a measurement noise vector at k time;
Figure BDA0003957658410000072
the attitude matrix output by the odometer represents the conversion relation between the carrier system b (k) at the moment k and the carrier system b (0) at the initial moment;
Figure BDA0003957658410000073
to represent
Figure BDA0003957658410000074
Is used to generate the inverse symmetric matrix.
And step S4: and performing Kalman filtering to obtain initial attitude error estimation and lever arm estimation:
Figure BDA0003957658410000075
P(k,k-1)＝Φ(k,k-1)P(k-1)Φ(k,k-1) T
K(k)＝P(k,k-1)H(k) T (H(k)P(k,k-1)H(k) T +R(k)) -1
Figure BDA0003957658410000076
P(k)＝(I-K(k)H(k))P(k,k-1)
wherein the content of the first and second substances,
Figure BDA0003957658410000077
and P (k, k-1) is state one-step prediction and its corresponding mean square error matrix;
Figure BDA0003957658410000078
and P (k) is the state estimation at the time k and the corresponding mean square error matrix; k (K) is a filtering gain array at the K moment; r (k) is a measurement noise variance matrix at the k moment.
Step S5: correcting the initial attitude by using the initial attitude error estimation feedback and setting the initial attitude error estimation to zero:
s5.1, the initial attitude is corrected by utilizing the initial attitude error estimation feedback:
Figure BDA0003957658410000079
Figure BDA00039576584100000710
wherein the content of the first and second substances,
Figure BDA00039576584100000711
estimating initial attitude error for time k
Figure BDA00039576584100000712
Corresponding transformation matrix representing the real initial time carrier system b 0 Initial time carrier system with time k estimation
Figure BDA00039576584100000713
The conversion relationship of (1);
Figure BDA00039576584100000714
the initial attitude matrix at the k time obtained after feedback correction represents the local horizontal geographic coordinate system n (0) where the carrier is located at the initial time and the initial time carrier system estimated at the k time
Figure BDA00039576584100000715
The conversion relationship of (1);
s5.2, zero setting initial attitude error estimation:
Figure BDA00039576584100000716
step S6: carrying out attitude alignment on the relative attitude of the odometer by utilizing initial attitude estimation to obtain an absolute attitude:
Figure BDA00039576584100000717
Figure BDA0003957658410000081
wherein the content of the first and second substances,
Figure BDA0003957658410000082
representing the conversion relation between a k moment carrier system b (k) and a k moment geographic coordinate system n (k) for the absolute attitude matrix of the odometer at the k moment after the attitude alignment;
Figure BDA0003957658410000083
and the conversion relation between the initial time geographic coordinate system n (0) and the k time geographic coordinate system n (k) is shown.
Step S7: calculating by using the absolute course of the double-antenna GNSS at the same time and the absolute attitude of the odometer after the attitude is aligned to obtain the installation deflection angle of the double-antenna GNSS and the carrier:
Figure BDA0003957658410000084
wherein the content of the first and second substances,
Figure BDA0003957658410000085
representing the conversion relation between a carrier system and a GNSS coordinate system for an installation deflection angle matrix of the dual-antenna GNSS and the carrier at the moment k;
Figure BDA0003957658410000086
and the k-time double-antenna GNSS absolute course matrix represents the conversion relation between a k-time GNSS coordinate system and a geographic coordinate system.
Step S8: and repeating the steps S2 to S7 until the initial posture and the lever arm converge to respective accurate quantities.
The effect of the invention is verified by a laser radar odometer/double-antenna GNSS space online calibration simulation experiment.
FIG. 5 is a schematic diagram illustrating a comparison between a GNSS trajectory and a lidar odometer trajectory in this embodiment. Fig. 6 is a graph showing the evaluation results of the lever arm in the embodiment. Fig. 7 is a heading and drift angle estimation result diagram of the initial time carrier system b (0) and the local horizontal geographic coordinate system n (0) where the initial time carrier is located in the embodiment. FIG. 8 is a diagram illustrating the results of the LIDAR system and dual-antenna GNSS system setup bias angle calculations in the illustrated embodiment. Simulation results show that the method can accurately, quickly and conveniently realize the space online calibration of the laser radar odometer and the dual-antenna GNSS.
It should be noted that the above-mentioned embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, and all equivalent substitutions or substitutions made on the basis of the above-mentioned technical solutions belong to the scope of the present invention.

Claims (8)

1. A odometer/dual-antenna GNSS space calibration method is characterized by comprising the following steps:
step S1: selecting an initial attitude error and a lever arm as state quantities, establishing a Kalman filtering state equation and discretizing;
step S2: converting the geographic coordinate of the GNSS measuring carrier into a geocentric rectangular coordinate;
and step S3: taking the difference value of the relative position of the odometer at the same moment and the position of the double-antenna GNSS after coordinate transformation as the observed quantity of Kalman filtering, and establishing a Kalman filtering measurement equation;
and step S4: performing Kalman filtering to obtain initial attitude error estimation and lever arm estimation;
step S5: correcting the initial attitude by using the initial attitude error estimation feedback and setting the initial attitude error estimation to be zero;
step S6: carrying out attitude alignment on the relative attitude of the odometer by utilizing the initial attitude to obtain an absolute attitude;
step S7: calculating the installation deflection angle of the double-antenna GNSS and the odometer by using the absolute attitude of the odometer after the absolute course and the attitude of the double-antenna GNSS at the same moment are aligned;
step S8: and repeating the steps S2 to S7 until the initial posture and the lever arm converge to respective accurate quantities.
2. The odometer/dual-antenna GNSS space calibration method according to claim 1, wherein the step S1 specifically includes the following processes:
s1.1, selecting an initial attitude error and a lever arm as state quantities, and establishing a Kalman filtering state equation:
Figure FDA0003957658400000011
wherein, X is a state vector,
Figure FDA0003957658400000012
delta phi is an initial attitude error vector, delta phi = [0 ] u ] Τ ，δφ u Is the heading deflection angle error, l is the carrier tie rod arm vector, l = [ l = x l y 0] Τ ，l x And l y The vector is the x-axis and y-axis shaft lever arm vector of the carrier system respectively; f is a system matrix, F =0 6×6 (ii) a W is the systematic noise vector, W =0 6×1 ；
S1.2 discretizes the equation of state:
X(k)＝Φ(k,k-1)X(k-1)
wherein X (k) is a state vector at the time of k; phi (k, k-1) is a state one-step transition matrix from the time k-1 to the time k, and phi (k, k-1) = I 4×4 。
3. The odometer/dual-antenna GNSS space calibration method according to claim 1, wherein the step S2 specifically includes the following processes:
measuring geographical coordinates of a carrier using GNSS
Figure FDA0003957658400000013
Converting to geocentric rectangular coordinates
Figure FDA0003957658400000014
Figure FDA0003957658400000021
Wherein, λ (k), L (k), h (k) are respectively longitude, latitude, altitude, R of GNSS measurement carrier at the moment of k N Is the curvature radius of the unitary-mortise ring,
Figure FDA0003957658400000022
e is the eccentricity of the earth
Figure FDA0003957658400000023
R e And R p Respectively a long half shaft and a short half shaft of the earth.
4. The odometer/dual-antenna GNSS space calibration method according to claim 1, wherein the step S3 specifically includes the following processes:
s3.1, taking the difference value of the relative position of the odometer at the same moment and the position of the dual-antenna GNSS after coordinate transformation as the observed quantity of Kalman filtering:
Figure FDA0003957658400000024
Figure FDA0003957658400000025
Figure FDA0003957658400000026
wherein Z (k) is a measurement vector at the moment k; setting the loading system to coincide with the coordinate system of the odometer;
Figure FDA0003957658400000027
the odometer position vector of the carrier at the moment k relative to the initial moment carrier system b (0);
Figure FDA0003957658400000028
representing the conversion relation between the initial time carrier system b (0) estimated at the time k-1 and the local horizontal geographic coordinate system n (0) where the initial time carrier is located;
Figure FDA00039576584000000216
the position matrix of the initial time carrier represents the conversion relation between a local horizontal geographic coordinate system n (0) where the initial time carrier is located and a geocentric earth-fixed rectangular coordinate system e;
Figure FDA0003957658400000029
the vector is a projection of a carrier GNSS position vector at the time k relative to the initial time in a geographical coordinate system n (0) at the initial time;
Figure FDA00039576584000000210
and
Figure FDA00039576584000000211
the geocentric rectangular coordinates of the carrier calculated in the step S2 are respectively the initial time and the k time;
s3.2, establishing a Kalman filtering measurement equation:
Z(k)＝H(k)X(k)+V(k)
Figure FDA00039576584000000212
wherein H (k) is a measurement matrix at the time k; v (k) is a measurement noise vector at the k moment;
Figure FDA00039576584000000213
the attitude matrix output by the odometer represents the conversion relation between the carrier system b (k) at the k moment and the carrier system b (0) at the initial moment;
Figure FDA00039576584000000214
to represent
Figure FDA00039576584000000215
Is used to generate the inverse symmetric matrix.
5. The odometer/dual-antenna GNSS space calibration method according to claim 1, wherein the step S4 specifically includes the following processes:
s4, kalman filtering is carried out to obtain initial attitude error estimation and lever arm estimation:
Figure FDA0003957658400000031
P(k,k-1)＝Φ(k,k-1)P(k-1)Φ(k,k-1) T
K(k)＝P(k,k-1)H(k) T (H(k)P(k,k-1)H(k) T +R(k)) -1
Figure FDA0003957658400000032
P(k)＝(I-K(k)H(k))P(k,k-1)
wherein the content of the first and second substances,
Figure FDA0003957658400000033
and P (k, k-1) is state one-step prediction and its corresponding mean square error matrix;
Figure FDA0003957658400000034
and P (k) is the state estimation at the time k and the corresponding mean square error matrix; k (K) is a filtering gain array at the K moment; r (k) is a measurement noise variance matrix at the k moment.
6. The odometer/dual-antenna GNSS space calibration method according to claim 1, wherein the step S5 specifically includes the following processes:
s5.1, correcting the initial attitude by using the estimation feedback of the initial attitude error:
Figure FDA0003957658400000035
Figure FDA0003957658400000036
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003957658400000037
estimating initial attitude error for time k
Figure FDA0003957658400000038
Corresponding transformation matrix representing the real initial time carrier system b 0 Initial time carrier system with time k estimation
Figure FDA0003957658400000039
The conversion relationship of (1);
Figure FDA00039576584000000310
the initial attitude matrix at the time k obtained after feedback correction represents a local horizontal geographic coordinate system n (0) where the initial time carrier is positioned and an initial time carrier system estimated at the time k
Figure FDA00039576584000000311
The conversion relationship of (c);
s5.2, zero setting initial attitude error estimation:
Figure FDA00039576584000000312
7. the odometer/dual-antenna GNSS space calibration method according to claim 1, wherein the step S6 specifically includes the following processes:
s6, carrying out attitude alignment on the relative attitude of the odometer by utilizing the initial attitude to obtain an absolute attitude:
Figure FDA00039576584000000313
Figure FDA00039576584000000314
wherein the content of the first and second substances,
Figure FDA0003957658400000041
representing the conversion relation between a k moment carrier system b (k) and a k moment geographic coordinate system n (k) for the k moment odometer absolute attitude matrix after attitude alignment;
Figure FDA0003957658400000042
and the conversion relation between the initial time geographic coordinate system n (0) and the k time geographic coordinate system n (k) is shown.
8. The odometer/dual-antenna GNSS space calibration method according to claim 1, wherein the step S7 specifically includes the following processes:
s7, calculating by using the absolute course of the double-antenna GNSS at the same time and the absolute attitude of the odometer after the attitude is aligned to obtain the installation deflection angle of the double-antenna GNSS and the carrier:
Figure FDA0003957658400000043
wherein the content of the first and second substances,
Figure FDA0003957658400000044
representing the conversion relation between a carrier system and a GNSS coordinate system for an installation deflection angle matrix of the dual-antenna GNSS and the carrier at the moment k;
Figure FDA0003957658400000045
and the k-time double-antenna GNSS absolute course matrix represents the conversion relation between a k-time GNSS coordinate system and a geographic coordinate system.
CN202211466306.7A 2022-11-22 2022-11-22 Odometer/dual-antenna GNSS space online calibration method Pending CN115790652A (en)

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Publication number Priority date Publication date Assignee Title
CN117111101A (en) * 2023-06-26 2023-11-24 北京航空航天大学 Fault detection method for eliminating lever effect of double-layer space-based navigation enhanced ad hoc network

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117111101A (en) * 2023-06-26 2023-11-24 北京航空航天大学 Fault detection method for eliminating lever effect of double-layer space-based navigation enhanced ad hoc network
CN117111101B (en) * 2023-06-26 2024-03-22 北京航空航天大学 Fault detection method for eliminating lever effect of double-layer space-based navigation enhanced ad hoc network

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