CN116222551A - Underwater navigation method and device integrating multiple data - Google Patents

Underwater navigation method and device integrating multiple data Download PDF

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Publication number
CN116222551A
CN116222551A CN202211494492.5A CN202211494492A CN116222551A CN 116222551 A CN116222551 A CN 116222551A CN 202211494492 A CN202211494492 A CN 202211494492A CN 116222551 A CN116222551 A CN 116222551A
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navigation system
integrated navigation
error
geomagnetic
integrated
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邓超凡
伍东凌
陈正想
吕冰
孟诚
窦柯
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Yichang Testing Technique Research Institute
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • 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
    • G01C21/005—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 with correlation of navigation data from several sources, e.g. map or contour matching
    • 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
    • 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
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/30—Assessment of water resources

Abstract

The invention discloses an underwater navigation method and device for fusing various data, wherein the method comprises the following steps: establishing a combined navigation system comprising a micro-inertial combined unit, a magnetic sensor and a depth sensor, and determining a state initial value of the combined navigation system; the micro-inertial combined unit forms a strapdown inertial navigation system, updates the state of the combined navigation system, and estimates the attitude error, the speed error and the position error of the combined navigation system at the current moment; processing geomagnetic data obtained by synchronous measurement of the magnetic sensor and geomagnetic field data of a target area to obtain longitude and latitude of a position where the integrated navigation system is located; constructing measurement information, and estimating Kalman filtering state quantity of the integrated navigation system; and correcting the output of the integrated navigation system in real time to obtain corrected attitude information, speed information and position information of the integrated navigation system. The method of the invention can obtain high-precision information.

Description

Underwater navigation method and device integrating multiple data
Technical Field
The invention relates to the technical field of navigation, in particular to an underwater navigation method and device for fusing various data.
Background
An autonomous underwater vehicle (Autonomous Underwater Vehicle, AUV) is an important device for marine exploration and development, and a high-precision and high-reliability navigation system is a key for realizing autonomous operation and safety recovery of the AUV.
Since inertial navigation solution errors accumulate over time and the accuracy of long-term operation decreases, it is necessary to perform error correction by using an assisted navigation technique.
The invention considers geomagnetic navigation as a passive navigation system, has the advantages of low cost, interference resistance, all regions, moderate navigation precision and the like, is not limited by areas with unobvious topographic features such as oceans, deserts and the like, is not influenced by weather, and can not radiate energy outwards, thereby having passivity. The problem of decline of the underwater long-time working precision of the inertial navigation system can be well compensated.
The invention adopts Kalman filtering to fuse the micro inertial measurement unit, the magnetic sensor and the depth sensor data, and obtains the gesture, the speed and the position information which are superior to those of an independent strapdown inertial navigation system and an independent geomagnetic matching navigation system.
Disclosure of Invention
In view of this, the invention provides an underwater navigation method and device integrating multiple data, which can provide high-precision position, speed and attitude information for an underwater vehicle, and errors can not accumulate with time, and external GPS signals and the like are not required to be received.
The present invention is so implemented as to solve the above-mentioned technical problems.
An underwater navigation method integrating multiple data, comprising:
step S1: establishing an integrated navigation system comprising a micro-inertial combined unit, a magnetic sensor and a depth sensor, and determining a state initial value of the integrated navigation system by utilizing the micro-inertial combined unit and the magnetic sensor to perform initial alignment;
step S2: the micro-inertial combined unit forms a strapdown inertial navigation system, updates the state of the combined navigation system, and estimates the attitude error, the speed error and the position error of the combined navigation system at the current moment;
step S3: processing geomagnetic data obtained by synchronous measurement of the magnetic sensor and geomagnetic field data of a target area, and performing geomagnetic matching calculation on the processed data to obtain longitude and latitude of a position where the integrated navigation system is located;
step S4: the longitude and latitude of the integrated navigation system, the integrated navigation system depth information output by the depth sensor of the integrated navigation system and the position error output by the strapdown inertial navigation system are obtained through calculation to form measurement information, so that the Kalman filtering state quantity of the integrated navigation system is estimated;
step S5: and correcting the output of the integrated navigation system in real time based on the estimated Kalman filtering state quantity to obtain corrected attitude information, speed information and position information of the integrated navigation system.
Preferably, the step S1 includes:
at the initial time, the following relationship exists:
Figure BDA0003965044920000021
wherein g is the gravity acceleration,
Figure BDA0003965044920000022
the three-axis output of the gravity acceleration under the carrier coordinate system is that the carrier is an installation carrier of the integrated navigation system, and the beta and the gamma are respectively the pitch angle and the roll angle of the carrier at the initial moment and are calculated according to a formula (2):
Figure BDA0003965044920000031
Figure BDA0003965044920000032
the carrier coordinate system and the navigation coordinate system are not coincident, at this time, the components of the earth magnetic field on each axis are overlapped, the components of the earth magnetic field measured by the magnetic sensor on the three axes of the carrier coordinate system are firstly calculated to be projected in the horizontal plane, and then the course angle alpha of the carrier at the initial moment is calculated, wherein:
Figure BDA0003965044920000033
α＝arctan2(m x ′,m y ′) (6)
wherein ,[mx m y m z ] T For three-axis output of the earth magnetic field in the carrier coordinate system, [ m ] x ′ m y ′] T The method comprises the steps of projecting an earth magnetic field on a navigation coordinate system horizontal plane;
the initial value of the state of the integrated navigation system is the initial time integrated navigation system gesture [ alpha, beta, gamma ], and the initial speed and the position of the integrated navigation system are given by the outside.
Preferably, the step S2 includes:
deducing a strapdown inertial navigation system error equation according to a strapdown inertial navigation system differential equation, establishing a state equation of the integrated navigation system based on the strapdown inertial navigation system error equation, and then establishing a measurement equation of the integrated navigation system; taking the attitude error, the speed error and the position error of the integrated navigation system as state variables of the integrated navigation system, correcting and updating the state variables of the integrated navigation system in real time by utilizing Kalman filtering based on a measurement equation of the integrated navigation system, and further carrying out state updating on the integrated navigation system to estimate the attitude error, the speed error and the position error of the integrated navigation system at the current moment;
the measurement equation of the integrated navigation system is as follows:
Z＝HX+v (15)
wherein, z= [ δl 'δλ' δh '], δl' is the difference between latitude information calculated according to the magnetic sensor and the latitude calculated by the strapdown inertial navigation system, δλ 'is the difference between longitude information calculated according to the magnetic sensor and the longitude calculated by the strapdown inertial navigation system, δh' is the difference between the depth calculated by the strapdown inertial navigation system and the depth output by the depth sensor, H is the combined navigation system measurement matrix, and v is the combined navigation system measurement noise matrix.
Preferably, the step S3 includes:
step S31: equidistant geomagnetic information is measured by utilizing a triaxial magnetic sensor, geomagnetic data and target area geomagnetic field data are obtained, and the geomagnetic data and the target area geomagnetic field data are processed; wherein, geomagnetic magnetic bits are expressed in a global geomagnetic field model by the following formula:
Figure BDA0003965044920000041
wherein: a is the reference sphere radius; r is the length from the center of the reference sphere to a certain calculation point in the earth space;
θ is the latitude and longitude, θ=pi 2-L mag ，L mag Is the magnetic field latitude of the point to be calculated;
Figure BDA0003965044920000042
and />
Figure BDA0003965044920000043
Is a gaussian coefficient; λ is the longitude of the point to be calculated; t1 is the order of the spherical harmonic series, t2 is the order of the spherical harmonic series, ++>
Figure BDA0003965044920000044
Called the schmitt normalized Legendre function; schmitt normalized Legendre function/>
Figure BDA0003965044920000045
Is calculated according to the following formula:
Figure BDA0003965044920000046
wherein d represents a derivative;
step S32: geomagnetic matching calculation is carried out on the processed data, so that longitude and latitude of the position where the integrated navigation system is located are obtained; and correcting the position of the strapdown inertial navigation system.
Preferably, the step S32 includes:
s321, outputting a certain number of initial reference position point sets by the strapdown inertial navigation system, and recording the initial reference position point sets as Ht; synchronously measuring by a magnetic sensor to obtain a geomagnetic data set of a corresponding position point, and recording the geomagnetic data set as Mt;
step S322: obtaining a position range estimated by the carrier according to the navigation precision and the estimated accumulated error of the strapdown inertial navigation system; obtaining a reference geomagnetic data set of the carrier in the position range from the priori high-precision geomagnetic chart carried by the carrier;
step S323: calculating the corresponding contour in the search area, i.e. C (Mt s ) S=1, 2, …, U is the number of sampling points in a certain matching area obtained by the strapdown inertial navigation system; s is the s-th sampling point on the matching path; solving the sum of square differences B of the longitude and latitude of each point on the contour line of the strapdown inertial navigation system output longitude and latitude and geomagnetic map d The least square difference and the smallest point are the closest Ht on the contour line s Point P of (2) s The method comprises the steps of carrying out a first treatment on the surface of the The square error sum is calculated as follows:
Figure BDA0003965044920000051
in the formula ：Ctx and Cty For pre-storing the longitude and latitude values of each point on the contour line obtained by geomagnetic chart, ht mx and Htmy For measuring points of geomagnetic sensorsInertial navigation output value; taking B d The smallest is used as the nearest point found on the contour line;
step S324: deriving a rigid transformation matrix T, rigid transformation to THt s ＝t+RHt s Wherein t is a translation vector, R is a rotation transformation matrix, and an objective function of the rigid transformation matrix is obtained as a nearest point set P s And rigid transformation point set THt s The relative distance between the two is minimum, and the relative distance formula is as follows:
Figure BDA0003965044920000052
step S325: transforming the initial set of points Ht according to a rigid transformation matrix s Obtaining the initial value THt of the next iteration operation s ；
Step S326: if the rate of change of the rigid transformation matrix T is less than a threshold, or the number of iterations exceeds a predetermined number of iterations, step S327 is entered;
ending the iteration and proceeding to step S327 if the rate of change of the rigid transformation matrix T is less than the threshold within the set maximum number of iterations;
if the iteration number is less than or equal to the predetermined iteration number, the process proceeds to step S324;
step S327: calculated THt s And for the position of the integrated navigation system obtained by geomagnetic matching, changing the rigid transformation matrix T into an optimal matching result, and correcting the position of the strapdown inertial navigation system according to the optimal matching result.
Preferably, the step S4 includes:
s41, calculating longitude and latitude of the integrated navigation system, integrated navigation system depth information output by a depth sensor of the integrated navigation system and position error output by the strapdown inertial navigation system to form measurement information;
step S42: and updating the time of the integrated navigation system, wherein the updating process comprises the following steps:
Figure BDA0003965044920000061
Figure BDA0003965044920000062
wherein ,
Figure BDA0003965044920000063
for the state estimation value of the integrated navigation system at the last moment, phi k,k-1 =i+fτ is the integrated navigation system state transition matrix, ++>
Figure BDA0003965044920000064
For updating the state at the current moment, P k-1 For the mean square error estimated value of the last moment, P k/k-1 To predict the mean square error in one step, Q k-1 A noise variance matrix of the integrated navigation system; when k=1, this represents the initial moment, +.>
Figure BDA0003965044920000065
and Pk-1 Initial alignment values for the integrated navigation system;
step S43: updating the system measurement of the integrated navigation system, wherein the updating process comprises the following steps:
Figure BDA0003965044920000066
Figure BDA0003965044920000067
P k ＝(I-K k H k )P k/k-1 (24)
wherein ,Rk For measuring noise variance matrix for system, K k For the Kalman filter gain matrix,
Figure BDA0003965044920000068
for current time state estimation, P k Estimating the mean square error of the current moment;
step S44: and estimating the Kalman filtering state quantity at the current moment as the real-time attitude error, the speed error and the position error of the integrated navigation system, and using the Kalman filtering state quantity as the Kalman filtering state quantity of the integrated navigation system.
Preferably, the step S5 includes:
by phi E 、φ N 、φ U Correcting a posture matrix:
Figure BDA0003965044920000071
Figure BDA0003965044920000072
wherein ,
Figure BDA0003965044920000073
for the posture correction matrix +.>
Figure BDA0003965044920000074
For the attitude matrix calculated according to the strapdown inertial navigation system,>
Figure BDA0003965044920000075
for the corrected pose matrix, phi E 、φ N 、φ U Respectively posture errors in three directions of northeast and north days; />
Figure BDA0003965044920000076
wherein ,
Figure BDA0003965044920000077
eastern direction, north direction and heaven direction speeds calculated for strapdown inertial navigation system, V E 、V N 、V U The corrected east, north and sky speeds;
Figure BDA0003965044920000078
wherein ,
Figure BDA0003965044920000079
the latitude, longitude and depth calculated for the strapdown inertial navigation system are the corrected latitude, longitude and depth;
the corrected attitude information, velocity information and position information are respectively characterized as corrected
Figure BDA00039650449200000710
V E 、V N 、V U And L, lambda, h.
The invention provides an underwater navigation device for fusing various data, which comprises:
an initialization module: the method comprises the steps of configuring to establish an integrated navigation system comprising a micro-inertial combined unit, a magnetic sensor and a depth sensor, and determining a state initial value of the integrated navigation system by utilizing the micro-inertial combined unit and the magnetic sensor to perform initial alignment;
an error estimation module: the micro inertial combined unit is configured to form a strapdown inertial navigation system, the state of the combined navigation system is updated, and the attitude error, the speed error and the position error of the combined navigation system at the current moment are estimated;
and a resolving module: the geomagnetic sensor is configured to process geomagnetic data obtained by synchronous measurement of the magnetic sensor and geomagnetic field data of a target area, and geomagnetic matching calculation is carried out on the processed data to obtain longitude and latitude of a position where the integrated navigation system is located;
the state quantity estimation module: the combined navigation system depth information output by the combined navigation system depth sensor and the position error output by the strapdown inertial navigation system are configured to form measurement information by the longitude and latitude of the combined navigation system obtained through calculation, so that the Kalman filtering state quantity of the combined navigation system is estimated;
and an output module: and the system is configured to correct the output of the integrated navigation system in real time based on the estimated Kalman filtering state quantity to obtain corrected attitude information, speed information and position information of the integrated navigation system.
The invention provides a computer readable storage medium, wherein a plurality of instructions are stored in the storage medium; the plurality of instructions are for loading and executing by a processor the method as described above.
The invention provides an electronic device, which is characterized by comprising:
a processor for executing a plurality of instructions;
a memory for storing a plurality of instructions;
wherein the plurality of instructions are for storage by the memory and loading and executing by the processor the method as described above.
The beneficial effects are that:
(1) The invention obtains various data based on Micro-inertial unit (Micro-Electro-Mechanical System Inertial Measurement Unit, MEMS IMU), magnetic sensor and depth sensor, and realizes the data fusion of MEMS IMU, magnetometer and depth gauge by Kalman filtering, thus obtaining high-precision attitude angle.
(2) The invention combines the advantages of geomagnetic navigation and inertial navigation, and has high navigation precision.
(3) The invention has small calculated amount and is easy to realize.
(4) The invention has simple resolving mode.
(5) The invention has good real-time performance.
Drawings
FIG. 1 is a schematic flow chart of an underwater navigation method integrating various data;
FIG. 2 is a schematic flow chart of another method for underwater navigation with multiple data fusion according to the present invention;
FIG. 3 is a flowchart of Kalman filtering according to the present invention;
fig. 4 is a schematic structural diagram of an underwater navigation device for fusing multiple data.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
As shown in fig. 1-2, the invention provides an underwater navigation method integrating multiple data, comprising the following steps:
step S1: establishing an integrated navigation system comprising a micro-inertial combined unit, a magnetic sensor and a depth sensor, and determining a state initial value of the integrated navigation system by utilizing the micro-inertial combined unit and the magnetic sensor to perform initial alignment;
step S2: the micro-inertial combined unit forms a strapdown inertial navigation system, updates the state of the combined navigation system, and estimates the attitude error, the speed error and the position error of the combined navigation system at the current moment;
step S3: processing geomagnetic data obtained by synchronous measurement of the magnetic sensor and geomagnetic field data of a target area, and performing geomagnetic matching calculation on the processed data to obtain longitude and latitude of a position where the integrated navigation system is located;
step S4: the longitude and latitude of the integrated navigation system, the integrated navigation system depth information output by the depth sensor of the integrated navigation system and the position error output by the strapdown inertial navigation system are obtained through calculation to form measurement information, so that the Kalman filtering state quantity of the integrated navigation system is estimated;
step S5: and correcting the output of the integrated navigation system in real time based on the estimated Kalman filtering state quantity to obtain corrected attitude information, speed information and position information of the integrated navigation system.
The step S1 includes:
under a quasi-static condition, the gravity acceleration has no projection component in the horizontal direction in a geographic coordinate system, and the triaxial acceleration sensor only outputs a measured value in the vertical downward direction, wherein the measured value is g; then there are:
Figure BDA0003965044920000101
wherein ,
Figure BDA0003965044920000102
triaxial output of gravitational acceleration in the carrier coordinate system, +.>
Figure BDA0003965044920000103
For navigating the coordinate transformation matrix from the coordinate system to the carrier coordinate system, [ 0g ]] T The three-axis output of the gravity acceleration under the navigation coordinate system is realized by the following steps that the carrier refers to an installation carrier (which can be an autonomous underwater vehicle or a carrier such as a water surface ship, an airplane and the like) of the combined navigation system, and the following steps are realized by expanding the following steps: />
Figure BDA0003965044920000104
Wherein, beta and gamma are the carrier pitch angle and roll angle respectively, and can be calculated according to the formula (2):
Figure BDA0003965044920000105
Figure BDA0003965044920000106
the carrier coordinate system and the navigation coordinate system are not coincident, at the moment, the components of the earth magnetic field on each axis are overlapped, the components of the earth magnetic field measured by the magnetic sensor on the three axes of the carrier coordinate system are firstly calculated to be projected in the horizontal plane, then the course angle alpha is solved, and the course angle, the pitch angle and the roll angle are used for calculation to obtain
Figure BDA0003965044920000107
I.e. the coordinate transformation matrix of the carrier coordinate system to the navigation coordinate system.
Figure BDA0003965044920000111
α＝arctan2(m x ′,m y ′) (6)
wherein ,[mx m y m z ] T For three-axis output of the earth magnetic field in the carrier coordinate system, [ m ] x ′m y ′] T The method comprises the steps of projecting an earth magnetic field on a navigation coordinate system horizontal plane;
the initial value of the state of the integrated navigation system is the gesture of the integrated navigation system at the initial moment, and the initial speed and the position are given by the outside.
In this embodiment, the pitch/roll angle calculated by formulas (3) and (4) is used to convert the magnetic sensor output in the carrier coordinate system into the navigation coordinate system, and then the azimuth angle is calculated according to the magnetic field in the navigation coordinate system, thereby calculating the coordinate transformation matrix from the carrier coordinate system to the navigation coordinate system
Figure BDA0003965044920000112
The step S2: the micro-inertial combined unit forms a strapdown inertial navigation system, updates the state of the combined navigation system, and estimates the attitude error, the speed error and the position error of the combined navigation system at the current moment, wherein:
the strapdown inertial navigation system comprises a strapdown inertial navigation system differential equation and a strapdown inertial navigation system error equation, wherein the strapdown inertial navigation system differential equation comprises a gesture differential equation, a speed differential equation and a position differential equation; the strapdown inertial navigation system error equation comprises an attitude error equation, a speed error equation and a position error equation.
The strapdown inertial navigation system comprises a strapdown inertial navigation system state equation and a strapdown inertial navigation system measurement equation.
And deducing a strapdown inertial navigation system error equation according to a strapdown inertial navigation system differential equation, taking the attitude error, the speed error and the position error of the integrated navigation system as the state variables of the integrated navigation system, establishing a state equation and a measurement equation, and carrying out real-time correction and update on the state variables of the system by using Kalman filtering.
The differential equation of the strapdown inertial navigation system is established by taking the northeast coordinate system as a navigation coordinate system.
The attitude differential equation is:
Figure BDA0003965044920000121
/>
in the formula, (. Times.) the vector is expressed as an antisymmetric matrix, i.e. there are
Figure BDA0003965044920000122
Figure BDA0003965044920000123
For the coordinate transformation matrix of the carrier coordinate system to the navigation coordinate system,/for the navigation coordinate system>
Figure BDA0003965044920000124
For theoretical output of gyroscope, +.>
Figure BDA0003965044920000125
For the projection of the angular velocity of rotation of the navigation coordinate system relative to the inertial coordinate system in the navigation coordinate system, +.>
Figure BDA0003965044920000126
The upper-marked dot number indicates the differentiation of the coordinate transformation matrix of the carrier coordinate system to the navigation coordinate system.
The velocity differential equation is:
Figure BDA0003965044920000127
in the formula ,
Figure BDA0003965044920000128
projection of the velocity of the carrier relative to the earth calculated for the strapdown inertial navigation system in the navigation coordinate system, +.>
Figure BDA0003965044920000129
Differential representing speed, ++>
Figure BDA00039650449200001210
For projection of the measured values of the three-axis acceleration sensor in the navigation coordinate system, +.>
Figure BDA00039650449200001211
Acceleration of gravity, ++>
Figure BDA00039650449200001212
For the projection of the angular velocity of the earth coordinate system relative to the navigation coordinate system under the navigation coordinate system, +.>
Figure BDA00039650449200001213
The projection in the navigation coordinate system is the angular velocity of the navigation coordinate system relative to the earth coordinate system.
The position differential equation is:
Figure BDA00039650449200001214
wherein L, lambda, h are latitude, longitude and depth, respectively, R M 、R N The main curvature radius of the meridian circle and the unitary circle along the earth are respectively,
Figure BDA00039650449200001215
respectively indicates the speeds in three directions of northeast, and +.>
Figure BDA00039650449200001216
The differentiation of latitude, longitude and depth, respectively.
Defining a deviation angle between a navigation coordinate system actually established by the strapdown inertial navigation system and an ideal navigation coordinate system as an attitude error:
φ n ＝[φ E φ N φ U ] T (10)
the attitude error equation is:
Figure BDA0003965044920000131
φ n is the attitude error phi of the strapdown inertial navigation system E 、φ N 、φ U Respectively, the posture errors in the three directions of northeast.
Figure BDA0003965044920000132
Error of angular velocity of the earth coordinate system relative to the navigation coordinate system,/->
Figure BDA0003965044920000133
For navigating the angular velocity of the coordinate system relative to the earth coordinate system epsilon n For the three-axis constant drift of the gyroscope under the navigation coordinate system, < >>
Figure BDA0003965044920000134
The differential is indicated by the superscript of the dot number for the differential of the attitude error of the strapdown inertial navigation system. />
The speed error equation is:
Figure BDA0003965044920000135
Figure BDA0003965044920000136
for speed error in three directions of northeast days, +.>
Figure BDA0003965044920000137
For the three-axis constant value drift phi of the acceleration sensor under the navigation coordinate system n For system attitude error, delta represents the error term, δv n Is a speed error.
The position error equation is:
Figure BDA0003965044920000138
wherein δL, δλ, δh are latitude, longitude and depth errors respectively,
Figure BDA0003965044920000139
is the differentiation of longitude errors, v E For eastern speed δv E Is the east speed error.
And establishing a mathematical model for the integrated navigation system, wherein the mathematical model comprises an integrated navigation system state equation and an integrated navigation system measurement equation.
The state equation of the integrated navigation system is as follows:
Figure BDA0003965044920000141
wherein F is an inertial navigation system state matrix calculated according to formulas (11) - (13), G is a combined navigation system noise distribution matrix, W is a system state noise matrix, and X is a system state variable.
Figure BDA0003965044920000142
wherein ,εx 、ε y 、ε z Is the three-axis constant value drift of the gyroscope under the carrier coordinate system,
Figure BDA0003965044920000143
is the three-axis constant value drift phi of the acceleration sensor under the carrier coordinate system E 、φ N 、φ U Is an attitude error. δV (delta V) E 、δV N 、δV U For northeast direction speed errors δl, δλ, δh are latitude, longitude and depth errors.
The state equation of the integrated navigation system is constructed by combining an error equation of the strapdown inertial navigation system.
The measurement equation of the integrated navigation system is as follows:
Z＝HX+v(15)
in z= [ δl 'δλ' δh '], δl' is the difference between longitude information calculated according to the magnetic sensor and longitude calculated by the strapdown inertial navigation system, δλ 'is the difference between latitude information calculated according to the magnetic sensor and latitude calculated by the strapdown inertial navigation system, δh' is the difference between depth calculated by the strapdown inertial navigation system and depth output by the depth sensor, H is a system measurement matrix, and v is a system measurement noise matrix.
Status updating of the integrated navigation system
Figure BDA0003965044920000144
Estimating the attitude error, the speed error and the position error of the integrated navigation system at the current moment, wherein the attitude error, the speed error and the position error are respectively +.>
Figure BDA0003965044920000145
Is the first nine elements of (2).
The step S3: processing geomagnetic data obtained by synchronous measurement of a magnetic sensor and geomagnetic field data of a target area, and performing geomagnetic matching calculation on the processed data to obtain longitude and latitude of a position where the integrated navigation system is located, wherein the method comprises the following steps:
step S31: equidistant geomagnetic information is measured by utilizing a triaxial magnetic sensor, geomagnetic data and target area geomagnetic field data are obtained, and the geomagnetic data and the target area geomagnetic field data are processed; wherein, geomagnetic magnetic bits are expressed in a global geomagnetic field model by the following formula:
Figure BDA0003965044920000151
wherein: a is the reference sphere radius; r is the length from the center of the reference sphere to a certain calculation point in the earth space; θ is the latitude and longitude, θ=pi/2-L mag ，L mag Is the magnetic field latitude of the point to be calculated;
Figure BDA0003965044920000152
and />
Figure BDA0003965044920000153
Is a gaussian coefficient; λ is the longitude of the point to be calculated; t1 is the order of the spherical harmonic series, t2 is the order of the spherical harmonic series, ++>
Figure BDA0003965044920000154
Called the schmitt normalized Legendre function. Style normalized Legendre function->
Figure BDA0003965044920000155
Is calculated according to the following formula:
Figure BDA0003965044920000156
wherein d represents a derivative;
step S32: geomagnetic matching calculation is carried out on the processed data, so that longitude and latitude of the position where the integrated navigation system is located are obtained; and correcting the position of the strapdown inertial navigation system.
The step S32 includes:
s321, outputting a certain number of initial reference position point sets by the strapdown inertial navigation system, and recording the initial reference position point sets as Ht; synchronously measuring by a magnetic sensor to obtain a geomagnetic data set of a corresponding position point, and recording the geomagnetic data set as Mt;
step S322: obtaining a position range estimated by the carrier according to the navigation precision and the estimated accumulated error of the strapdown inertial navigation system; obtaining a reference geomagnetic data set of the carrier in the position range from the priori high-precision geomagnetic chart carried by the carrier;
step S323: calculating the corresponding contour in the search area, i.e. C (Mt s ) S=1, 2, …, U is the number of sampling points in a certain matching area obtained by the strapdown inertial navigation system; s is the s-th sampling point on the matching path; solving the sum of square differences B of the longitude and latitude of each point on the contour line of the strapdown inertial navigation system output longitude and latitude and geomagnetic map d The least square difference and the smallest point are the closest Ht on the contour line s Point P of (2) s The method comprises the steps of carrying out a first treatment on the surface of the The square error sum is calculated as follows:
Figure BDA0003965044920000161
in the formula ：Ctx and Cty For pre-storing the longitude and latitude values of each point on the contour line obtained by geomagnetic chart, ht mx and Htmy Inertial navigation output value of the geomagnetic sensor measuring point; taking B d The smallest one is the closest point found on the contour.
Step S324: deriving a rigid transformation matrix T, rigid transformation to THt s ＝t+RHt s Wherein t is a translation vector, R is a rotation transformation matrix, and an objective function of the rigid transformation matrix is obtained as a nearest point set P s And rigid transformation point set THt s The relative distance between the two is minimum, and the relative distance formula is as follows:
Figure BDA0003965044920000162
step S325: transforming the initial set of points Ht according to a rigid transformation matrix s Obtaining the initial value THt of the next iteration operation s ；
Step S326: if the rate of change of the rigid transformation matrix T is less than a threshold, or the number of iterations exceeds a predetermined number of iterations, step S327 is entered;
ending the iteration and proceeding to step S327 if the rate of change of the rigid transformation matrix T is less than the threshold within the set maximum number of iterations;
if the iteration number is less than or equal to the predetermined iteration number, the process proceeds to step S324;
step S327: and changing the rigid transformation matrix T into an optimal matching result, and correcting the position of the strapdown inertial navigation system according to the optimal matching result.
As shown in fig. 3, the step S4: the longitude and latitude of the integrated navigation system, the integrated navigation system depth information output by the depth sensor of the integrated navigation system and the position error output by the strapdown inertial navigation system are obtained through calculation to form measurement information, so that the Kalman filtering state quantity of the integrated navigation system is estimated, and the method comprises the following steps:
s41, calculating longitude and latitude of the integrated navigation system, integrated navigation system depth information output by a depth sensor of the integrated navigation system and position error output by the strapdown inertial navigation system to form measurement information;
step S42: and updating the time of the integrated navigation system, wherein the updating process comprises the following steps:
Figure BDA0003965044920000171
Figure BDA0003965044920000172
wherein ,
Figure BDA0003965044920000173
for the system state estimated value at the last moment, phi k,k-1 =i+fτ is the system state transition matrix, +.>
Figure BDA0003965044920000174
For updating the state at the current moment, P k-1 For the mean square error estimated value of the last moment, P k/k-1 To predict the mean square error in one step, Q k-1 A system noise variance matrix; when k=1, this represents the initial moment, +.>
Figure BDA0003965044920000175
and Pk-1 And (3) initial alignment values for the integrated navigation system.
Step S43: updating the system measurement of the integrated navigation system, wherein the updating process comprises the following steps:
K k ＝P k/k-1 H k T (H k P k/k-1 H k T +R k ) -1 (22)
Figure BDA0003965044920000176
P k ＝(I-K k H k )P k/k-1 (24)
wherein ,Rk For measuring noise variance matrix for system, K k For the Kalman filter gain matrix,
Figure BDA0003965044920000177
for current time state estimation, P k Estimating the mean square error of the current moment;
step S44: and estimating the Kalman filtering state quantity at the current moment as the real-time attitude error, the speed error and the position error of the integrated navigation system, and using the Kalman filtering state quantity as the Kalman filtering state quantity of the integrated navigation system.
The step S5: correcting the output of the integrated navigation system in real time based on the estimated Kalman filtering state quantity to obtain corrected attitude information, speed information and position information of the integrated navigation system, wherein the method comprises the following steps:
by phi E 、φ N 、φ U Correcting a posture matrix:
Figure BDA0003965044920000178
Figure BDA0003965044920000181
wherein ,
Figure BDA0003965044920000182
for the posture correction matrix +.>
Figure BDA0003965044920000183
For the attitude matrix calculated according to the strapdown inertial navigation system,>
Figure BDA0003965044920000184
for corrected gesture matrix。
Figure BDA0003965044920000185
wherein ,
Figure BDA0003965044920000186
eastern direction, north direction and heaven direction speeds calculated for strapdown inertial navigation system, V E 、V N 、V U The corrected east, north and sky speeds.
Figure BDA0003965044920000187
wherein ,
Figure BDA0003965044920000188
the latitude, longitude and depth calculated for the strapdown inertial navigation system are the corrected latitude, longitude and depth;
the corrected attitude information, velocity information and position information are respectively characterized as corrected
Figure BDA0003965044920000189
V E 、V N 、V U And L, lambda, h;
the corrected posture information of the integrated navigation system is that
Figure BDA00039650449200001810
Namely, the attitude matrix of the integrated navigation system, and the corrected position information is L, lambda and h, which respectively represent the latitude, longitude and altitude of the integrated navigation system.
The invention also provides an underwater navigation device for fusing various data, as shown in fig. 4, the device comprises:
an initialization module: the method comprises the steps of configuring to establish an integrated navigation system comprising a micro-inertial combined unit, a magnetic sensor and a depth sensor, and determining a state initial value of the integrated navigation system by utilizing the micro-inertial combined unit and the magnetic sensor to perform initial alignment;
an error estimation module: the micro inertial combined unit is configured to form a strapdown inertial navigation system, the state of the combined navigation system is updated, and the attitude error, the speed error and the position error of the combined navigation system at the current moment are estimated;
and a resolving module: the geomagnetic sensor is configured to process geomagnetic data obtained by synchronous measurement of the magnetic sensor and geomagnetic field data of a target area, and geomagnetic matching calculation is carried out on the processed data to obtain longitude and latitude of a position where the integrated navigation system is located;
the state quantity estimation module: the combined navigation system depth information output by the combined navigation system depth sensor and the position error output by the strapdown inertial navigation system are configured to form measurement information by the longitude and latitude of the combined navigation system obtained through calculation, so that the Kalman filtering state quantity of the combined navigation system is estimated;
and an output module: and the system is configured to correct the output of the integrated navigation system in real time based on the estimated Kalman filtering state quantity to obtain corrected attitude information, speed information and position information of the integrated navigation system.
The above specific embodiments merely describe the design principle of the present invention, and the shapes of the components in the description may be different, and the names are not limited. Therefore, the technical scheme described in the foregoing embodiments can be modified or replaced equivalently by those skilled in the art; such modifications and substitutions do not depart from the spirit and technical scope of the invention, and all of them should be considered to fall within the scope of the invention.

Claims (10)

1. An underwater navigation method integrating multiple data, characterized in that the method comprises the following steps:
step S1: establishing an integrated navigation system comprising a micro-inertial combined unit, a magnetic sensor and a depth sensor, and determining a state initial value of the integrated navigation system by utilizing the micro-inertial combined unit and the magnetic sensor to perform initial alignment;
step S2: the micro-inertial combined unit forms a strapdown inertial navigation system, updates the state of the combined navigation system, and estimates the attitude error, the speed error and the position error of the combined navigation system at the current moment;
step S3: processing geomagnetic data obtained by synchronous measurement of the magnetic sensor and geomagnetic field data of a target area, and performing geomagnetic matching calculation on the processed data to obtain longitude and latitude of a position where the integrated navigation system is located;
step S4: the longitude and latitude of the integrated navigation system, the integrated navigation system depth information output by the depth sensor of the integrated navigation system and the position error output by the strapdown inertial navigation system are obtained through calculation to form measurement information, so that the Kalman filtering state quantity of the integrated navigation system is estimated;
step S5: and correcting the output of the integrated navigation system in real time based on the estimated Kalman filtering state quantity to obtain corrected attitude information, speed information and position information of the integrated navigation system.
2. The method according to claim 1, wherein the step S1 includes:
at the initial time, the following relationship exists:
Figure FDA0003965044910000011
wherein g is the gravity acceleration,
Figure FDA0003965044910000012
the three-axis output of the gravity acceleration under the carrier coordinate system is that the carrier is an installation carrier of the integrated navigation system, and the beta and the gamma are respectively the pitch angle and the roll angle of the carrier at the initial moment and are calculated according to a formula (2):
Figure FDA0003965044910000021
Figure FDA0003965044910000022
the carrier coordinate system and the navigation coordinate system are not coincident, at this time, the components of the earth magnetic field on each axis are overlapped, the components of the earth magnetic field measured by the magnetic sensor on the three axes of the carrier coordinate system are firstly calculated to be projected in the horizontal plane, and then the course angle alpha of the carrier at the initial moment is calculated, wherein:
m x ′＝m x cosβ+m y sinβsinγ-m z sinβcosγ
m y ′＝m y cosγ+m z sinγ (5)
α＝arctan2(m x ′,m y ′) (6)
wherein ,[mx m y m z ] T For three-axis output of the earth magnetic field in the carrier coordinate system, [ m ] x ′ m y ′] T The method comprises the steps of projecting an earth magnetic field on a navigation coordinate system horizontal plane;
the initial value of the state of the integrated navigation system is the initial time integrated navigation system gesture [ alpha, beta, gamma ], and the initial speed and the position of the integrated navigation system are given by the outside.
3. The method according to claim 2, wherein the step S2 includes:
deducing a strapdown inertial navigation system error equation according to a strapdown inertial navigation system differential equation, establishing a state equation of the integrated navigation system based on the strapdown inertial navigation system error equation, and then establishing a measurement equation of the integrated navigation system; taking the attitude error, the speed error and the position error of the integrated navigation system as state variables of the integrated navigation system, correcting and updating the state variables of the integrated navigation system in real time by utilizing Kalman filtering based on a measurement equation of the integrated navigation system, and further carrying out state updating on the integrated navigation system to estimate the attitude error, the speed error and the position error of the integrated navigation system at the current moment;
the measurement equation of the integrated navigation system is as follows:
Z＝HX+v (15)
wherein, z= [ δl 'δλ' δh '], δl' is the difference between latitude information calculated according to the magnetic sensor and the latitude calculated by the strapdown inertial navigation system, δλ 'is the difference between longitude information calculated according to the magnetic sensor and the longitude calculated by the strapdown inertial navigation system, δh' is the difference between the depth calculated by the strapdown inertial navigation system and the depth output by the depth sensor, H is the combined navigation system measurement matrix, and v is the combined navigation system measurement noise matrix.
4. A method according to any one of claims 1-3, wherein step S3 comprises:
step S31: equidistant geomagnetic information is measured by utilizing a triaxial magnetic sensor, geomagnetic data and target area geomagnetic field data are obtained, and the geomagnetic data and the target area geomagnetic field data are processed; wherein, geomagnetic magnetic bits are expressed in a global geomagnetic field model by the following formula:
Figure FDA0003965044910000031
wherein: a is the reference sphere radius; r is the length from the center of the reference sphere to a certain calculation point in the earth space;
θ is the latitude and longitude, θ=pi/2-L mag ，L mag Is the magnetic field latitude of the point to be calculated;
Figure FDA0003965044910000032
and />
Figure FDA0003965044910000033
Is a gaussian coefficient; λ is the longitude of the point to be calculated; t1 is the order of the spherical harmonic series, t2 is the order of the spherical harmonic series, ++>
Figure FDA0003965044910000034
Called the schmitt normalized Legendre function; style normalized Legendre function->
Figure FDA0003965044910000035
Is calculated according to the following formula:
Figure FDA0003965044910000036
wherein d represents a derivative;
step S32: geomagnetic matching calculation is carried out on the processed data, so that longitude and latitude of the position where the integrated navigation system is located are obtained; and correcting the position of the strapdown inertial navigation system.
5. The method of claim 4, wherein the step S32 includes:
s321, outputting a certain number of initial reference position point sets by the strapdown inertial navigation system, and recording the initial reference position point sets as Ht; synchronously measuring by a magnetic sensor to obtain a geomagnetic data set of a corresponding position point, and recording the geomagnetic data set as Mt;
step S322: obtaining a position range estimated by the carrier according to the navigation precision and the estimated accumulated error of the strapdown inertial navigation system; obtaining a reference geomagnetic data set of the carrier in the position range from the priori high-precision geomagnetic chart carried by the carrier;
step S323: calculating the corresponding contour in the search area, i.e. C (Mt s ) S=1, 2, …, U is the number of sampling points in a certain matching area obtained by the strapdown inertial navigation system; s is the s-th sampling point on the matching path; solving the sum of square differences B of the longitude and latitude of each point on the contour line of the strapdown inertial navigation system output longitude and latitude and geomagnetic map d The least square difference and the smallest point are the closest Ht on the contour line s Point P of (2) s The method comprises the steps of carrying out a first treatment on the surface of the The square error sum is calculated as follows:
Figure FDA0003965044910000041
in the formula ：Ctx and Cty For pre-storing the longitude and latitude values of each point on the contour line obtained by geomagnetic chart, ht mx and Htmy Inertial navigation output value of the geomagnetic sensor measuring point; taking B d The smallest is used as the nearest point found on the contour line;
step S324: deriving a rigid transformation matrix T, rigid transformation to THt s ＝t+RHt s Wherein t is a translation vector, R is a rotation transformation matrix, and an objective function of the rigid transformation matrix is obtained as a nearest point set P s And rigid transformation point set THt s The relative distance between the two is minimum, and the relative distance formula is as follows:
Figure FDA0003965044910000042
step S325: transforming the initial set of points Ht according to a rigid transformation matrix s Obtaining the initial value THt of the next iteration operation s ；
Step S326: if the rate of change of the rigid transformation matrix T is less than a threshold, or the number of iterations exceeds a predetermined number of iterations, step S327 is entered;
ending the iteration and proceeding to step S327 if the rate of change of the rigid transformation matrix T is less than the threshold within the set maximum number of iterations;
if the iteration number is less than or equal to the predetermined iteration number, the process proceeds to step S324;
step S327: calculated THt s And for the position of the integrated navigation system obtained by geomagnetic matching, changing the rigid transformation matrix T into an optimal matching result, and correcting the position of the strapdown inertial navigation system according to the optimal matching result.
6. The method according to claim 5, wherein the step S4 includes:
s41, calculating longitude and latitude of the integrated navigation system, integrated navigation system depth information output by a depth sensor of the integrated navigation system and position error output by the strapdown inertial navigation system to form measurement information;
step S42: and updating the time of the integrated navigation system, wherein the updating process comprises the following steps:
Figure FDA0003965044910000051
Figure FDA0003965044910000052
wherein ,
Figure FDA0003965044910000053
for the state estimation value of the integrated navigation system at the last moment, phi k,k-1 =i+fτ is the integrated navigation system state transition matrix, ++>
Figure FDA0003965044910000054
For updating the state at the current moment, P k-1 For the mean square error estimated value of the last moment, P k/k-1 To predict the mean square error in one step, Q k-1 A noise variance matrix of the integrated navigation system; when k=1, the initial time is indicated, at this time
Figure FDA0003965044910000055
and Pk-1 Initial alignment values for the integrated navigation system;
step S43: updating the system measurement of the integrated navigation system, wherein the updating process comprises the following steps:
K k ＝P k/k-1 H k T (H k P k/k-1 H k T +R k ) -1 (22)
Figure FDA0003965044910000056
P k ＝(I-K k H k )P k/k-1 (24)
wherein ,Rk For measuring noise variance matrix for system, K k For the Kalman filter gain matrix,
Figure FDA0003965044910000057
for current time state estimation, P k Estimating the mean square error of the current moment;
step S44: and estimating the Kalman filtering state quantity at the current moment as the real-time attitude error, the speed error and the position error of the integrated navigation system, and using the Kalman filtering state quantity as the Kalman filtering state quantity of the integrated navigation system.
7. The method of claim 6, said step S5 comprising:
by phi E 、φ N 、φ U Correcting a posture matrix:
Figure FDA0003965044910000061
Figure FDA0003965044910000062
wherein ,
Figure FDA0003965044910000063
for the posture correction matrix +.>
Figure FDA0003965044910000064
For the attitude matrix calculated according to the strapdown inertial navigation system,>
Figure FDA0003965044910000065
for the corrected pose matrix, phi E 、φ N 、φ U Respectively posture errors in three directions of northeast and north days;
Figure FDA0003965044910000066
wherein ,
Figure FDA0003965044910000067
eastern direction, north direction and heaven direction speeds calculated for strapdown inertial navigation system, V E 、V N 、V U The corrected east, north and sky speeds;
Figure FDA0003965044910000068
wherein ,
Figure FDA0003965044910000069
the latitude, longitude and depth calculated for the strapdown inertial navigation system are the corrected latitude, longitude and depth;
the corrected attitude information, velocity information and position information are respectively characterized as corrected
Figure FDA00039650449100000610
V E 、V N 、V U And L, lambda, h.
8. An underwater navigation device that fuses a plurality of data, the device comprising:
an initialization module: the method comprises the steps of configuring to establish an integrated navigation system comprising a micro-inertial combined unit, a magnetic sensor and a depth sensor, and determining a state initial value of the integrated navigation system by utilizing the micro-inertial combined unit and the magnetic sensor to perform initial alignment;
an error estimation module: the micro inertial combined unit is configured to form a strapdown inertial navigation system, the state of the combined navigation system is updated, and the attitude error, the speed error and the position error of the combined navigation system at the current moment are estimated;
and a resolving module: the geomagnetic sensor is configured to process geomagnetic data obtained by synchronous measurement of the magnetic sensor and geomagnetic field data of a target area, and geomagnetic matching calculation is carried out on the processed data to obtain longitude and latitude of a position where the integrated navigation system is located;
the state quantity estimation module: the combined navigation system depth information output by the combined navigation system depth sensor and the position error output by the strapdown inertial navigation system are configured to form measurement information by the longitude and latitude of the combined navigation system obtained through calculation, so that the Kalman filtering state quantity of the combined navigation system is estimated;
and an output module: and the system is configured to correct the output of the integrated navigation system in real time based on the estimated Kalman filtering state quantity to obtain corrected attitude information, speed information and position information of the integrated navigation system.
9. A computer-readable storage medium having stored therein a plurality of instructions; the plurality of instructions for loading and executing by a processor the method of any of claims 1-7.
10. An electronic device, the electronic device comprising:
a processor for executing a plurality of instructions;
a memory for storing a plurality of instructions;
wherein the plurality of instructions are for storage by the memory and loading and executing by the processor the method of any of claims 1-7.
CN202211494492.5A 2022-11-25 2022-11-25 Underwater navigation method and device integrating multiple data Pending CN116222551A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117268372A (en) * 2023-11-21 2023-12-22 北京理工大学前沿技术研究院 INS/GNSS integrated navigation method and system integrating magnetic navigation information

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117268372A (en) * 2023-11-21 2023-12-22 北京理工大学前沿技术研究院 INS/GNSS integrated navigation method and system integrating magnetic navigation information
CN117268372B (en) * 2023-11-21 2024-02-20 北京理工大学前沿技术研究院 INS/GNSS integrated navigation method and system integrating magnetic navigation information

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