CN114252089A - Combined calibration method for DVL speed measurement error - Google Patents

Combined calibration method for DVL speed measurement error Download PDF

Info

Publication number
CN114252089A
CN114252089A CN202111164821.5A CN202111164821A CN114252089A CN 114252089 A CN114252089 A CN 114252089A CN 202111164821 A CN202111164821 A CN 202111164821A CN 114252089 A CN114252089 A CN 114252089A
Authority
CN
China
Prior art keywords
dvl
carrier
inertial navigation
speed
coordinate system
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202111164821.5A
Other languages
Chinese (zh)
Other versions
CN114252089B (en
Inventor
黄科
姜校亮
可伟
韩袁昭
牛亚辉
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Hebei Hanguang Heavy Industry Ltd
Original Assignee
Hebei Hanguang Heavy Industry Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Hebei Hanguang Heavy Industry Ltd filed Critical Hebei Hanguang Heavy Industry Ltd
Priority to CN202111164821.5A priority Critical patent/CN114252089B/en
Priority claimed from CN202111164821.5A external-priority patent/CN114252089B/en
Publication of CN114252089A publication Critical patent/CN114252089A/en
Application granted granted Critical
Publication of CN114252089B publication Critical patent/CN114252089B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • 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

Landscapes

  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Manufacturing & Machinery (AREA)
  • Navigation (AREA)

Abstract

The combined calibration method for the DVL speed measurement error comprises the steps that the moving speed of a DVL measurement carrier is converted from a DVL coordinate system to an inertial navigation coordinate system, and the moving speed of the carrier in the inertial navigation coordinate system is obtained; designing a Kalman filter for combined calibration of the DVL speed measurement error based on the difference between the motion speed of the DVL measurement carrier and the motion speed of the carrier in the inertial navigation coordinate system; and calibrating the DVL velocity measurement error parameters according to the combination of the DVL velocity measurement error calibrated Kalman filter and observability of the inertial navigation system to obtain the real motion velocity of the carrier. Before the inertia/DVL combined navigation, the accuracy of the combined navigation system can be improved by calibrating the DVL speed measurement error.

Description

Combined calibration method for DVL speed measurement error
Technical Field
The invention belongs to the technical field of inertial navigation, and particularly relates to a combined calibration method for a DVL speed measurement error.
Background
The inertial navigation is a calculation method for calculating the attitude, the speed and the position of a carrier by using a gyroscope and an accelerometer to measure the angular velocity and the linear acceleration of the carrier on the basis of the Newton classical mechanics theory. The inertial navigation system can complete the navigation and positioning tasks only by the measured value of the inertial sensor of the inertial navigation system without the help of external information, and has autonomy and concealment which cannot be compared with other navigation means. As an indispensable navigation means, inertial navigation is widely used in many fields, especially in the military field. Because of a dead reckoning method, the speed error of the inertial navigation system is increased along with the increase of time, and the positioning accuracy of the system is further influenced. Therefore, in some situations requiring long navigation and positioning, such as autonomous underwater vehicles, it is necessary to provide velocity information to the system by means of a doppler velocity log (hereinafter referred to as DVL).
However, the output of the DVL is three components of the moving speed of the carrier in the DVL coordinate system, and the components need to be converted into the inertial navigation system coordinate system for navigation. Due to mounting inaccuracies, there is a certain error angle between the two coordinate systems and the output of the DVL itself has a certain error. These errors have a significant effect on the navigation system and therefore must be calibrated in advance for the combined inertial/DVL navigation system.
Disclosure of Invention
The invention overcomes one of the defects of the prior art, and provides a combined calibration method of the DVL speed measurement error, which can improve the precision of the combined navigation system by calibrating the DVL speed measurement error before the inertia/DVL combined navigation.
According to an aspect of the present disclosure, the present invention provides a combined calibration method for DVL velocity measurement errors, the method including:
converting the movement speed of the DVL measurement carrier from the DVL coordinate system to an inertial navigation coordinate system to obtain the carrier movement speed in the inertial navigation coordinate system;
designing a Kalman filter for combined calibration of the DVL speed measurement error based on the difference between the motion speed of the DVL measurement carrier and the motion speed of the carrier in the inertial navigation coordinate system;
and calibrating the DVL velocity measurement error parameters according to the combination of the DVL velocity measurement error calibrated Kalman filter and observability of the inertial navigation system to obtain the real motion velocity of the carrier.
In a possible implementation manner, the converting the moving speed of the DVL measurement carrier to an inertial navigation coordinate system to obtain a carrier moving speed in the inertial navigation coordinate system includes:
the carrier motion speed under the inertial navigation coordinate system is as follows:
Figure BDA0003291337190000021
wherein, VdMeasuring the moving speed of the carrier for DVL, determining δ k as the scale coefficient error between the moving speed of the carrier for DVL and the moving speed of the carrier under an inertial navigation coordinate system,
Figure BDA0003291337190000022
is a transfer matrix from the DVL coordinate system to the inertial navigation coordinate system.
In a possible implementation manner, the Kalman filter calibrated by the combination of the DVL velocity measurement errors is:
Z＝Vb-Vd
＝(1+δk)(I-η×)Vd-Vd
＝δkVd-(1+δk)η×Vd
＝δkVd+Vd×[(1+δk)η]
＝HX，
wherein Z ═ Vx-VX Vy-VY Vz-VZ]TIs the measurement vector of the inertial navigation system, H ═ Vd Vd×]3×4Is a measurement matrix of the inertial navigation system, where X ═ δ k (1+ δ k) Φ (1+ δ k) θ (1+ δ k) ψ]TAnd the system state vector is composed of the DVL speed measurement error parameters.
In one possible implementation, the condition of observability of the inertial navigation system is: there is a certain moment in time at which,
matrix array
Figure BDA0003291337190000023
The reverse-direction-changing material can be used,
wherein the content of the first and second substances,
Figure BDA0003291337190000024
matrix array
Figure BDA0003291337190000031
And matrix- (V)d×)2Not full rank.
In a possible implementation manner, the real motion speed of the carrier is in the calibration process, and the motion speed and the transfer matrix of the DVL measurement carrier are obtained by inertial navigation combination navigation
Figure BDA0003291337190000032
The product of (a).
The combined calibration method for the DVL speed measurement error comprises the steps that the moving speed of a DVL measurement carrier is converted from a DVL coordinate system to an inertial navigation coordinate system, and the moving speed of the carrier in the inertial navigation coordinate system is obtained; designing a Kalman filter for combined calibration of the DVL speed measurement error based on the difference between the motion speed of the DVL measurement carrier and the motion speed of the carrier in the inertial navigation coordinate system; and calibrating the DVL velocity measurement error parameters according to the combination of the DVL velocity measurement error calibrated Kalman filter and observability of the inertial navigation system to obtain the real motion velocity of the carrier. Before the inertia/DVL combined navigation, the accuracy of the combined navigation system can be improved by calibrating the DVL speed measurement error.
Drawings
The accompanying drawings are included to provide a further understanding of the technology or prior art of the present application and are incorporated in and constitute a part of this specification. The drawings expressing the embodiments of the present application are used for explaining the technical solutions of the present application, and should not be construed as limiting the technical solutions of the present application.
Fig. 1 illustrates a schematic diagram of a combined calibration principle of DVL velocity measurement error according to an embodiment of the present disclosure;
FIG. 2 is a flow chart illustrating a combined DVL velocity measurement error calibration method according to an embodiment of the present disclosure;
3a-3d respectively show combined calibration parameter diagrams of DVL velocimetry errors according to an embodiment of the present disclosure;
fig. 4a-4d respectively show an uncertainty diagram of a combined calibration parameter of a DVL velocimetry error according to an embodiment of the present disclosure.
Detailed Description
The following detailed description of the embodiments of the present invention will be provided with reference to the accompanying drawings and examples, so that how to apply the technical means to solve the technical problems and achieve the corresponding technical effects can be fully understood and implemented. The embodiments and the features of the embodiments can be combined without conflict, and the technical solutions formed are all within the scope of the present invention.
Additionally, the steps illustrated in the flow charts of the figures may be performed in a computer such as a set of computer-executable instructions. Also, while a logical order is shown in the flow diagrams, in some cases, the steps shown or described may be performed in an order different than here.
Fig. 1 shows a schematic diagram of a combined calibration principle of DVL velocity measurement errors according to an embodiment of the present disclosure.
As shown in FIG. 1, in the combined navigation system of the strapdown inertial measurement unit and the GPS, the parameters of the strapdown inertial measurement unit and the GPS are filtered by the combined navigation filter of the strapdown inertial measurement unit and the GPS to obtain the velocity V of the inertial navigation coordinate systembThe velocity information measured by the DVL is the velocity V of the DVL coordinate systemdVelocity V of inertial navigation coordinate systembAnd DVL coordinate system velocity VdThe calibrated DVL error parameter is obtained by calibrating the DVL calibration filter, and then the DVL error parameter is used for VdThe accuracy of the DVL measurement can be improved by performing the correction. The main performance indexes of the strapdown inertial measurement unit, the GPS and the DVL are shown in the table 1.
Figure BDA0003291337190000041
Fig. 2 shows a flowchart of a combined DVL velocity measurement error calibration method according to an embodiment of the present disclosure.
As shown in fig. 2, the method may include:
step S1: and converting the moving speed of the DVL measurement carrier from the DVL coordinate system to the inertial navigation coordinate system to obtain the carrier moving speed in the inertial navigation coordinate system.
The carrier motion speed under the inertial navigation coordinate system is as follows:
Figure BDA0003291337190000042
wherein, VdMeasuring the moving speed of the carrier for DVL, determining δ k as the scale coefficient error between the moving speed of the carrier for DVL and the moving speed of the carrier under an inertial navigation coordinate system,
Figure BDA0003291337190000043
is a transfer matrix from the DVL coordinate system to the inertial navigation coordinate system.
As shown in fig. 1, assuming that the inertial navigation system coordinate system of the navigation system combining the strapdown inertial navigation set and the GPS is a b-system (referred to as O-XYZ coordinate system), and the DVL (doppler velocity log) coordinate system is a d-system (referred to as O-XYZ coordinate system), the transfer matrix from the d-system (DVL coordinate system) to the b-system (inertial navigation system) is:
Figure BDA0003291337190000051
where ψ, φ, and θ are the heading angle, pitch angle, and roll angle from the d-system (DVL coordinate system) to the b-system (inertial navigation system), respectively.
Generally, when an inertial navigation system and a DVL are installed, in order to ensure that a d system (DVL coordinate system) approximately coincides with a b system (inertial navigation system), that is, euler angles are small angles, a DVL velocity measurement error model may be approximately:
Figure BDA0003291337190000052
in the formula: eta ═ phi theta psi]T。
Speed V of DVL outputd＝[Vx Vy Vz]TAnd the true velocity V of the carrierb＝[VX VY VZ]TApart from the coordinate transformation relation, the difference is a scale coefficient error delta k, i.e.
Figure BDA0003291337190000053
This is the mathematical model of the DVL velocimetry error.
Step S2: and designing a Kalman filter for combined calibration of the DVL speed measurement error based on the difference between the motion speed of the DVL measurement carrier and the motion speed of the carrier in the inertial navigation coordinate system.
The Kalman filter calibrated by the combination of the DVL speed measurement errors is as follows:
Z＝Vb-Vd
＝(1+δk)(I-η×)Vd-Vd
＝δkVd-(1+δk)η×Vd
＝δkVd+Vd×[(1+δk)η]
＝HX，
wherein Z ═ Vx-VX Vy-VY Vz-VZ]TIs the measurement vector of the inertial navigation system, H ═ Vd Vd×]3×4Is a measurement matrix of the inertial navigation system, where X ═ δ k (1+ δ k) Φ (1+ δ k) θ (1+ δ k) ψ]TAnd the system state vector is composed of the DVL speed measurement error parameters. The speed information output by the inertial navigation system can be prevented from containing large errors and not meeting the calibration requirement, so that the speed output by the inertial/GPS combined navigation system is used as the real speed of the carrier.
The discretization state equation of the filter is as follows: xk/k-1＝ΦXk-1，
Since δ k and η are both constant valuesIf the error is detected, the discretization state one-step transfer matrix of the inertial navigation integrated navigation system is phi ═ I4×4The system noise covariance matrix is Q ═ 0, and the measurement noise is the noise of DVL.
Step S3: and calibrating the DVL velocity measurement error parameters according to the combination of the DVL velocity measurement error calibrated Kalman filter and observability of the inertial navigation system to obtain the real motion velocity of the carrier.
The fully considerable requirements of the inertial navigation system (inertial navigation combination system) at the time k are as follows: there is a time n, such that the following matrix is invertible:
Figure BDA0003291337190000061
wherein the content of the first and second substances,
Figure BDA0003291337190000062
matrix array
Figure BDA0003291337190000063
And matrix- (V)d×)2Not full rank.
If the carrier velocity of the inertial navigation system does not change under the DVL coordinate system, the inertial navigation system is not completely observable. Therefore, the carrier of the inertial navigation system only changes the course or does acceleration and deceleration maneuvering, and the observability of the inertial navigation system cannot be changed. The inertial navigation system is only fully appreciable when the inertial navigation system carrier velocity changes in the DVL coordinate system (or carrier coordinate system, the transfer relationship between which is fixed). It is therefore possible to design a calibration path: after the inertial navigation system is electrified and aligned, the power system applies forward motion to the inertial navigation system carrier, and the component of the motion speed under the system b is Vb1＝[0 vy 0]T(ii) a After a certain time, the power system maintains the forward speed and applies a transverse speed to the carrier, and the component under the b system is Vb2＝[vx vy 0]T. Therefore, the system is completely observable, and the speed measurement error parameter of the DVL can be calibrated.
The initial parameters of the calibration algorithm are as follows, and can be adjusted appropriately according to actual conditions, and all the calculation data are calculated by adopting standard dimensions, for example, P0＝diag[(0.1)2、(5°)2、(5°)2、(5)2]，Q＝0， R＝diag[(0.01m/s)2、(0.01m/s)2、(0.01m/s)2]. As can be seen from the algorithm, only the measurement update is needed for Kalman filtering update. Velocity V obtained by inertial/GPS combined navigation in calibration processnMultiplying by the attitude matrix Cb nTrue velocity V as a carrierb。
3a-3d respectively show combined calibration parameter diagrams of DVL velocimetry errors according to an embodiment of the present disclosure; fig. 4a-4d respectively show an uncertainty diagram of a combined calibration parameter of a DVL velocimetry error according to an embodiment of the present disclosure.
For example, the carrier moves to the east at a constant speed of 10m/s within 0-300 s; the east speed of the carrier is unchanged for 300-310 s, and the north speed is increased from 0 to 10 m/s; if the carrier keeps constant-speed motion for 310-610 s, the simulation result of the obtained combined calibration parameters of the DVL speed measurement error is shown in the attached drawing3a～3dShown, and the obtained simulation result of the uncertainty of the combined calibration parameter of the DVL velocity measurement error is shown in the figure4a～4dAs shown in fig. 2 to 3, the DVL velocity measurement error parameter calibration method of the present disclosure designs a calibration path corresponding to a DVL velocity measurement error by analyzing observability of the system, and ensures accuracy of the combined navigation result.
The combined calibration method for the DVL speed measurement error comprises the steps that the moving speed of a DVL measurement carrier is converted from a DVL coordinate system to an inertial navigation coordinate system, and the moving speed of the carrier in the inertial navigation coordinate system is obtained; designing a Kalman filter for combined calibration of the DVL speed measurement error based on the difference between the motion speed of the DVL measurement carrier and the motion speed of the carrier in the inertial navigation coordinate system; and calibrating the DVL velocity measurement error parameters according to the combination of the DVL velocity measurement error calibrated Kalman filter and observability of the inertial navigation system to obtain the real motion velocity of the carrier. Before the inertia/DVL combined navigation, the accuracy of the combined navigation system can be improved by calibrating the DVL speed measurement error.
Although the embodiments of the present invention have been described above, the above descriptions are only for the convenience of understanding the present invention, and are not intended to limit the present invention. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. A combined calibration method for DVL speed measurement errors is characterized by comprising the following steps:
converting the movement speed of the DVL measurement carrier from the DVL coordinate system to an inertial navigation coordinate system to obtain the carrier movement speed in the inertial navigation coordinate system;
designing a Kalman filter for combined calibration of the DVL speed measurement error based on the difference between the motion speed of the DVL measurement carrier and the motion speed of the carrier in the inertial navigation coordinate system;
and calibrating the DVL velocity measurement error parameters according to the combination of the DVL velocity measurement error calibrated Kalman filter and observability of the inertial navigation system to obtain the real motion velocity of the carrier.
2. The combined calibration method according to claim 1, wherein the converting the moving velocity of the DVL measurement carrier into an inertial navigation coordinate system to obtain the moving velocity of the carrier in the inertial navigation coordinate system comprises:
the carrier motion speed under the inertial navigation coordinate system is as follows:
Figure FDA0003291337180000011
wherein, VdMeasuring the moving speed of the carrier for DVL, determining δ k as the scale coefficient error between the moving speed of the carrier for DVL and the moving speed of the carrier under an inertial navigation coordinate system,
Figure FDA0003291337180000012
is a transfer matrix from the DVL coordinate system to the inertial navigation coordinate system.
3. The combined calibration method according to claim 1, wherein the Kalman filter for combined calibration of the DVL velocimetry error is:
Z＝Vb-Vd
＝(1+δk)(I-η×)Vd-Vd
＝δkVd-(1+δk)η×Vd
＝δkVd+Vd×[(1+δk)η]
＝HX，
wherein Z ═ Vx-VX Vy-VY Vz-VZ]TIs the measurement vector of the inertial navigation system, H ═ Vd Vd×]3×4Is a measurement matrix of the inertial navigation system, where X ═ δ k (1+ δ k) Φ (1+ δ k) θ (1+ δ k) ψ]TAnd the system state vector is composed of the DVL speed measurement error parameters.
4. The combined calibration method according to claim 1, wherein the condition of observability of the inertial navigation system is: there is a certain moment in time at which,
matrix array
Figure FDA0003291337180000013
The reverse-direction-changing material can be used,
wherein the content of the first and second substances,
Figure FDA0003291337180000014
matrix array
Figure FDA0003291337180000021
And matrix- (V)d×)2Not full rank.
5. A combined calibration method according to claim 1, characterized in that the real speed of motion of the carrierIn the calibration process, the motion speed and the transfer matrix of the DVL measurement carrier are obtained by the inertial navigation combination navigation
Figure FDA0003291337180000022
The product of (a).
CN202111164821.5A 2021-09-30 Combined calibration method for DVL speed measurement errors Active CN114252089B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111164821.5A CN114252089B (en) 2021-09-30 Combined calibration method for DVL speed measurement errors

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111164821.5A CN114252089B (en) 2021-09-30 Combined calibration method for DVL speed measurement errors

Publications (2)

Publication Number Publication Date
CN114252089A true CN114252089A (en) 2022-03-29
CN114252089B CN114252089B (en) 2024-05-31

Family

ID=

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103389115A (en) * 2013-07-26 2013-11-13 哈尔滨工程大学 Integrated error calibrating method of SINS/DVL (strapdown inertial navigation system/doppler velocity sonar) combined navigation system
CN106908086A (en) * 2017-04-14 2017-06-30 北京理工大学 A kind of modification method of Doppler log range rate error
CN108871379A (en) * 2018-07-04 2018-11-23 北京理工大学 A kind of DVL range rate error online calibration method
CN110031882A (en) * 2018-08-02 2019-07-19 哈尔滨工程大学 A kind of outer measurement information compensation method based on SINS/DVL integrated navigation system
CN111323050A (en) * 2020-03-19 2020-06-23 哈尔滨工程大学 Strapdown inertial navigation and Doppler combined system calibration method
CN112197789A (en) * 2020-08-14 2021-01-08 北京自动化控制设备研究所 INS/DVL installation error calibration method based on QUEST
CN112504298A (en) * 2020-11-25 2021-03-16 东南大学 GNSS-assisted DVL error calibration method

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103389115A (en) * 2013-07-26 2013-11-13 哈尔滨工程大学 Integrated error calibrating method of SINS/DVL (strapdown inertial navigation system/doppler velocity sonar) combined navigation system
CN106908086A (en) * 2017-04-14 2017-06-30 北京理工大学 A kind of modification method of Doppler log range rate error
CN108871379A (en) * 2018-07-04 2018-11-23 北京理工大学 A kind of DVL range rate error online calibration method
CN110031882A (en) * 2018-08-02 2019-07-19 哈尔滨工程大学 A kind of outer measurement information compensation method based on SINS/DVL integrated navigation system
CN111323050A (en) * 2020-03-19 2020-06-23 哈尔滨工程大学 Strapdown inertial navigation and Doppler combined system calibration method
CN112197789A (en) * 2020-08-14 2021-01-08 北京自动化控制设备研究所 INS/DVL installation error calibration method based on QUEST
CN112504298A (en) * 2020-11-25 2021-03-16 东南大学 GNSS-assisted DVL error calibration method

Similar Documents

Publication Publication Date Title
CN107588769B (en) Vehicle-mounted strapdown inertial navigation, odometer and altimeter integrated navigation method
CN113311411B (en) Laser radar point cloud motion distortion correction method for mobile robot
JP4876204B2 (en) Small attitude sensor
CN111323050B (en) Strapdown inertial navigation and Doppler combined system calibration method
CA2510714C (en) System for navigation redundancy
US11215475B2 (en) Experimental calibration method for redundant inertial measurement unit
CN105136145A (en) Kalman filtering based quadrotor unmanned aerial vehicle attitude data fusion method
CN109945859B (en) Kinematics constraint strapdown inertial navigation method of self-adaptive H-infinity filtering
JP2012173190A (en) Positioning system and positioning method
CN107741240B (en) Adaptive initial alignment method of combined inertial navigation system suitable for communication-in-moving
Wongwirat et al. A position tracking experiment of mobile robot with inertial measurement unit (imu)
CN111812737A (en) Integrated system for underwater navigation and gravity measurement
US20130085712A1 (en) Inertial sensing input apparatus and method thereof
CN114252089A (en) Combined calibration method for DVL speed measurement error
CN114252089B (en) Combined calibration method for DVL speed measurement errors
CN114397480B (en) Acoustic Doppler velocimeter error estimation method, device and system
CN114019954B (en) Course installation angle calibration method, device, computer equipment and storage medium
CN115523919A (en) Nine-axis attitude calculation method based on gyro drift optimization
CN113484542B (en) Single-point rapid calibration method for three-dimensional velocimeter
CN115371706A (en) Lei cluster strapdown inertial navigation error model unified formula based on Rodrigues parameters
CN112013849A (en) Autonomous positioning method and system for surface ship
JPH0949737A (en) Navigation signal outputting method
CN110879066A (en) Attitude calculation algorithm and device and vehicle-mounted inertial navigation system
RU2634071C1 (en) Method for determining navigational parameters and strapdown inertial navigation system for its implementation
CN110082805A (en) A kind of 3 D locating device and method

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant