CN115371706A - Lei cluster strapdown inertial navigation error model unified formula based on Rodrigues parameters - Google Patents

Lei cluster strapdown inertial navigation error model unified formula based on Rodrigues parameters Download PDF

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CN115371706A
CN115371706A CN202211080154.7A CN202211080154A CN115371706A CN 115371706 A CN115371706 A CN 115371706A CN 202211080154 A CN202211080154 A CN 202211080154A CN 115371706 A CN115371706 A CN 115371706A
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inertial navigation
strapdown inertial
error model
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navigation error
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李开龙
朱天高
常路宾
覃方君
李文魁
钱镭源
黄春福
车浩
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Naval University of Engineering PLA
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    • 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
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention relates to a Lee group strapdown inertial navigation error model unification based on a Rodrigues parameter, which comprises the following steps: firstly, an attitude updating equation based on the Rodrigues parameter and the corrected Rodrigues parameter is deduced, and a unified Ledrigue strapdown inertial navigation error model based on the Rodrigues parameter is provided by combining a Ledrigue inertial navigation error model. The model can express a Lee group strapdown inertial navigation error model based on Euler angles, quaternions, rodrigues parameters and corrected Rodrigues parameters into a unified form. The method comprises the steps of comparing a lie group strapdown inertial navigation error model based on the Rodrigue parameters and corrected Rodrigue parameters with a lie group strapdown inertial navigation error model based on Euler angles and quaternions, and comparing the advantages and disadvantages of the four models through experiments.

Description

Lee group strapdown inertial navigation error model unified form based on Rodrigues parameters
Technical Field
The invention relates to the technical field of navigation, in particular to a unified Lei swarm strapdown inertial navigation error model based on a Rodrigues parameter.
Background
The strapdown inertial navigation system mainly comprises two sensors, namely a gyroscope and an accelerometer, and high-precision navigation positioning is realized through dead reckoning on the basis of Newton's motion law. A gyroscope and acceleration of the strapdown inertial navigation system are fixedly connected to a motion carrier, and linear velocity information and angular velocity information of the motion carrier are sensitive. Under the condition of giving initial navigation information, the self-contained calculation of navigation parameters such as attitude, speed and position can be realized by utilizing the linear acceleration and the angular acceleration output by the gyroscope and the accelerometer. Compared with other navigation modes, the strapdown inertial navigation system has the advantages of strong autonomy, high reliability, good concealment, comprehensive output of navigation information, all-weather work and the like, and is widely applied to the fields of aviation, aerospace, navigation and the like.
The working principle of strapdown inertial navigation is integral calculation, and positioning errors of the strapdown inertial navigation are continuously accumulated along with time under the influence of a plurality of error sources such as installation errors, device errors and initial errors, so that the calculation accuracy of navigation parameters is reduced. This process is relatively slow, but the navigation accuracy during long voyage is degraded, and the long voyage task cannot be independently completed. Therefore, in order to overcome the disadvantage of strapdown inertial navigation, information fusion and modern filtering technologies are often used to fuse data of two or more navigation systems, so that the advantages of multiple sensors are fully utilized to realize long-time high-precision navigation positioning, which is combined navigation. In many integrated navigation systems, strapdown inertial navigation is taken as a core, and other navigation modes such as satellite navigation, doppler log navigation and the like are taken as the integrated navigation of an auxiliary navigation system, which is the most common and the best effect, and the integrated navigation becomes the most widely applied dominant integrated mode in the fields of aerospace, navigation and land use.
As a dead reckoning system, a strapdown inertial navigation system needs initial attitude, speed, position and other information before entering inertial navigation resolving and integrated navigation, otherwise, subsequent performance is greatly influenced, and the initial information is obtained by initial alignment. The initial speed, position and other information are easy to obtain, and can be bound by external auxiliary equipment such as a global satellite navigation system, a Doppler log, a milemeter and the like, so how to obtain an accurate initial attitude in an initial alignment stage is a serious difficulty in the alignment technology research.
The conventional initial alignment process generally performs a coarse alignment and then a fine alignment. In the course of coarse alignment, the attitude of the carrier is generally regarded as a constant value, and is obtained by an analytic method by directly utilizing the attitude relationship between the output of the gyroscope and the accelerometer and the rotational angular velocity and gravity information of the earth. The purpose of coarse alignment is to initialize the attitude of the inertial navigation system and enable the attitude error to reach a small-angle error state, so that the establishment of a classical inertial navigation linear error equation is ensured. The fine alignment is performed by using an inertial navigation error equation as a state model and adopting a state estimation method with the aid of external observed quantities. However, since the strapdown inertial navigation system is fixed on the moving carrier, its output must couple the angular motion and linear motion information of the carrier itself and the related interference information, so that the traditional coarse alignment method cannot effectively obtain the coarse attitude of the carrier, and the fine alignment using the coarse alignment as the necessary condition cannot be completed normally. In addition, for ships, under certain emergency scenes and complex sea conditions, strapdown inertial navigation does not have the objective condition of static alignment, the coarse alignment cannot meet the requirement of a small misalignment angle required by fine alignment, and the fine alignment cannot be normally performed. Therefore, the research on the nonlinear initial alignment of the movable base under the condition of a large misalignment angle is very necessary, and the method is helpful for improving the emergency starting capability of ships, the emergency treatment of guided weapons and the survival striking capability, and has important theoretical research and application values.
And combining a group theory, simultaneously bringing the posture and the speed of the strapdown inertial navigation into a group, constructing a new error amount, and establishing a Lei-swarm-based strapdown inertial navigation error model. Currently, a large number of researches are carried out on a Lei group strapdown inertial navigation error model based on an Euler angle and a Lei group strapdown inertial navigation error model based on a quaternion, and compared with the posture representation of the Euler angle and the quaternion, the posture representation of the Rodrigue parameter has the advantages of small calculated amount, good filtering consistency, global non-singularity and the like. Therefore, the invention mainly develops research around a plum-group strapdown inertial navigation error model based on Rodrigues Parameters (RP) and Modified Rodrigues Parameters (RP), and compared with the plum-group strapdown inertial navigation error model based on Euler angles and quaternions, the invention has the advantages of better estimation precision, smaller calculated amount and the like. In addition, a unified lie group strapdown inertial navigation error model is provided, all the lie group strapdown inertial navigation error models based on the Euler angle, the quaternion, the Rodrigue parameter and the corrected Rodrigue parameter can be included, and the consistency of theoretical research is achieved.
Disclosure of Invention
In view of the above problems, the present invention aims to provide a unified form of a lie group strapdown inertial navigation error model with a rodgerge parameter, which aims to enable a ship to perform fast and high-precision dynamic start under a large misalignment angle condition, so as to overcome the defects of the existing literature on the research of a combined navigation model under the large misalignment condition. The model can rapidly complete high-precision nonlinear integrated navigation in a short time under the condition of large misalignment, and meets the requirement of high-precision integrated navigation.
A Lee group strapdown inertial navigation error model unification based on a Rodrigues parameter comprises the following steps: the method comprises the following steps of providing a plum group strapdown inertial navigation error model based on the Rodrigue parameters and the corrected Rodrigue parameters, establishing a unified plum group strapdown inertial navigation error model containing the Euler angles, the quaternion, the Rodrigue parameters and the corrected Rodrigue parameters, and comparing the advantages and the disadvantages of the four models through experiments, wherein the method specifically comprises the following steps:
1) Analyzing the posture representation of the Rodrigues parameters, wherein the posture representation of the Rodrigues parameters is mainly divided into two types of posture estimation of the Rodrigues parameters and posture estimation of correction Rodrigues parameters;
2) Analyzing the lie group strapdown inertial navigation error model, simultaneously bringing the attitude error and the speed error into a group, and constructing a new lie group strapdown inertial navigation error model;
3) Deducing a Lei swarm strapdown inertial navigation error model based on the Rodrigue parameters and a Lei swarm strapdown inertial navigation error model based on the corrected Rodrigue parameters based on the definition of the Rodrigue parameters and the attitude errors of the corrected Rodrigue parameters;
4) According to the conversion relation among the Euler angle, the quaternion, the Rodrigues parameter and the corrected Rodrigues parameter, a unified Lei group strapdown inertial navigation error model is provided, and the four Lei group strapdown inertial navigation error models can be represented at the same time;
5) And (3) comparing the performances of the Liqun strapdown inertial navigation error model based on the Euler angle, the quaternion, the Rodrigue parameter and the corrected Rodrigue parameter through two groups of vehicle-mounted experiments.
The invention mainly aims at a high-precision emergency starting scene of a ship under a large misalignment angle condition, provides a Lee strapdown inertial navigation error model based on a Lee strapdown inertial navigation error model and a Lee strapdown inertial navigation error model system including an Euler angle, a quaternion, a Rodrigue parameter and a modified Rodrigue parameter by combining a Rodrigue parameter and a posture representation method for modifying the Rodrigue parameter. Two groups of vehicle-mounted experiments prove that the performance of the Li-swarm strapdown inertial navigation error model based on the Rodrigue parameters and the corrected Rodrigue parameters is superior to that of the Li-swarm strapdown inertial navigation error model based on the Euler angle and the quaternion, and particularly the Li-swarm strapdown inertial navigation error model based on the Rodrigue parameters and the corrected Rodrigue parameters has more obvious performance advantage under the condition of larger initial heading angle. The method has extremely important significance for emergency starting of ships under large misalignment conditions, and has strong theoretical research and application values.
Drawings
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
FIG. 1 is a schematic block diagram of a carrier system quaternion attitude error based nonlinear error model and a navigation system quaternion attitude error based nonlinear error model according to the present invention;
FIG. 2 is a vehicle-mounted experimental trace diagram of the present invention;
FIG. 3 shows the initial misalignment angle of [10 °;10 degrees; course angle estimation error curve diagram under 30 °;
FIG. 4 shows the initial misalignment angle of [20 °;20 degrees; heading angle estimation error curve under 60 °;
FIG. 5 shows the initial misalignment angle of [30 °;30 degrees; heading angle estimation error plot at 90 ° ].
Detailed Description
In order that the objects and advantages of the invention will be more clearly understood, the invention is further described below with reference to examples; it should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only for explaining the technical principle of the present invention, and do not limit the scope of the present invention.
Referring to fig. 1 to 5, in order to describe the systematic shape of the error model of the lie group strapdown inertial navigation based on the rodgers parameter in detail, the error model of the lie group strapdown inertial navigation based on the rodgers parameter is given as follows:
1. euler angle-based plum-swarm strapdown inertial navigation attitude error model
The traditional strapdown inertial navigation attitude error model is
Figure BDA0003832669140000041
If the attitude and the speed are simultaneously included in one group, a new state quantity can be constructed
Figure BDA0003832669140000042
A new error state quantity can be obtained
Figure BDA0003832669140000043
Wherein
Figure BDA0003832669140000044
When the misalignment angle is wrong
Figure BDA0003832669140000051
Taking a minimum value, the following relationship exists
Figure BDA0003832669140000052
Thus, a plum-swarm strapdown inertial navigation error model based on Euler angles can be obtained
Figure BDA0003832669140000053
Figure BDA0003832669140000054
Figure BDA0003832669140000055
In the above formula
Figure BDA0003832669140000056
Figure BDA0003832669140000057
In the formula, the superscript n represents a navigation system, b represents a carrier system, and the physical meaning of the relevant quantities is as follows:
Figure BDA0003832669140000058
represents a directional cosine matrix from b to n,
Figure BDA0003832669140000059
the angular velocity of the carrier relative to the inertial frame (system i) which is the output of the gyroscope,
Figure BDA00038326691400000510
is the angular velocity of the earth's rotation,
Figure BDA00038326691400000511
is the sum of the acceleration caused by the rotation of the earth and the angular velocity caused by the motion of the carrier on the earth's surface, g n Is the acceleration of gravity;
Figure BDA00038326691400000512
for the actual output carrier angular velocity of the gyroscope,
Figure BDA00038326691400000513
is the inertial navigation angular velocity with the error amount,
Figure BDA00038326691400000514
is the actual output gravitational acceleration;
Figure BDA00038326691400000515
in order to measure the error for the gyroscope,
Figure BDA00038326691400000516
for accelerometer measurementsThe error is a function of the number of bits,
Figure BDA00038326691400000517
to calculate the error;
I 3 is a 3 × 3 identity matrix, R M Radius of the earth meridian, R N The radius of the earth-unitary mortise ring;
2. quaternion-based lie group strapdown inertial navigation attitude error model
If the attitude is expressed by quaternion, a quaternion-based lie strapdown inertial navigation error model can be constructed
Attitude error equation:
Figure BDA0003832669140000061
Figure BDA0003832669140000062
Figure BDA0003832669140000063
the velocity error equation:
Figure BDA0003832669140000064
position error equation:
Figure BDA0003832669140000065
3. lei group strapdown inertial navigation attitude error model based on Rodrigues parameters
Definition of
Figure BDA0003832669140000066
For the definition of the attitude error in the form of RP,
Figure BDA0003832669140000067
for the attitude error definition in MRP form, the Rodrigues parameter and the corrected Rodrigues parameter attitude error can be represented by the attitude error in quaternion form
Figure BDA0003832669140000068
Quaternion form attitude errors can also be represented by RP and MRP attitude errors as follows:
Figure BDA0003832669140000069
attitude error matrix in known quaternion form
Figure BDA00038326691400000610
There are the following conversion relationships
Figure BDA00038326691400000611
Definition of
Figure BDA00038326691400000612
And
Figure BDA00038326691400000613
the attitude error matrixes are respectively in the form of a Rodrigues parameter and the form of a modified Rodrigues parameter, the RP and the MRP are firstly converted into quaternions, and then the quaternions are substituted into the formula to obtain the attitude error matrix
Figure BDA00038326691400000614
And
Figure BDA00038326691400000615
according to the conversion relation among the RP, the MRP and the quaternion, the attitude error models based on the RP and the MRP are respectively
Figure BDA0003832669140000071
4. Lei group strapdown inertial navigation attitude error model unified formula based on Rodrigues parameters
Unified lie group strapdown inertial navigation attitude error model adopting attitude error matrix
Figure BDA0003832669140000072
Expressing the attitude error, the differential equation of the attitude error matrix can be obtained
Figure BDA0003832669140000073
The unified lie group strapdown inertial navigation attitude error model is obtained by
Figure BDA0003832669140000074
And
Figure BDA0003832669140000075
and substituting to obtain the above Liqun strapdown inertial navigation attitude error model based on the Euler angle, the quaternion, the Rodrigue parameter and the corrected Rodrigue parameter.
In addition, the speed error of the unity is defined as tau v Then the velocity error differential equation of unity is
Figure BDA0003832669140000076
A uniform differential equation of position and velocity of
Figure BDA0003832669140000077
The experimental verification method comprises the following steps:
1) For the sake of convenience of representation of these four models, these four models are designated as SE (3) -Euler, SE (3) -Quat, SE (3) -RP, and SE (3) -MRP, respectively. For the four models, the selection of the state quantity is specifically expressed as:
SE(3)-Euler：
Figure BDA0003832669140000078
SE(3)-Quat：
Figure BDA0003832669140000081
SE(3)-RP：
Figure BDA0003832669140000082
SE(3)-MRP：
Figure BDA0003832669140000083
in the formula, epsilon b In order to make the gyro drift in a constant value,
Figure BDA0003832669140000084
for accelerometer constant drift, SE (3) -Euler represents a Lewy group strapdown inertial navigation error model based on Euler angles, SE (3) -Quat represents a quaternion-based Lewy group strapdown inertial navigation error model, SE (3) -RP represents a Lewy group strapdown inertial navigation error model based on Rodrigue parameters, and SE (3) -MRP represents a modified Rodrigue parameter-based Lewy group strapdown inertial navigation error model
2) Selecting the observed quantity, wherein the speed and the position are used as the observed quantity of the combined navigation:
Figure BDA0003832669140000085
in the formula (I), the compound is shown in the specification,
Figure BDA0003832669140000086
for velocity and position information resolved by inertial navigation, z GPS Reference information for velocity and position obtained by satellite navigation.
3) And (4) carrying out a vehicle-mounted integrated navigation experiment, and analyzing and comparing the performances of the 4 Liqun strapdown inertial navigation error models. A set of consumption-level inertial navigation is arranged in the vehicle and used for measuring output information of a gyroscope and an acceleration sensor, the constant drift of the gyroscope is 0.3 degree/h, and the zero offset of the accelerometer is 20 mu g. The vehicle roof is provided with a GPS antenna for receiving satellite signals, the speed error of the GPS is 0.1m/s, and the position error is 10m. The sampling frequencies of inertial navigation and GPS are 200Hz and 1Hz respectively. In addition, a set of positioning and attitude determination system (POS system) is also arranged on the vehicle to provide an attitude reference, and the constant drift of a gyroscope in the POS system is 0.01 degree/h. The experiment is carried out on an open road, the time is about 800s, the track is shown in figure 2, a blue mark point is a starting point, and a green mark point is an end point. The GPS signal is received well in the movement process, the speed and the position measured by the GPS are used as observed quantities to carry out combined navigation, and the system noise and the noise measurement method are set according to the sensor index and the empirical value.
Initial error of inertial navigation system: the initial error of the strapdown inertial navigation system mainly comprises an initial attitude error, an initial speed error and an initial position error. The main application scenario of the invention is under the condition that the initial attitude error is a large misalignment angle, so the initial attitude error is set as the large misalignment angle, and the initial speed error and the initial position error are set according to experience. The parameters are set as follows:
initial error:
attitude error: the pitch angle, roll angle and course angle are respectively 10 degrees; 10 degrees; 30 ° ], [20 ° ]; 20 degrees; 60 ° ] and [30 °;30 degrees; 90 degree ]
Speed error: the speed errors in the northeast are all 1m/s
Position error: the errors of latitude, longitude and altitude position are all 10m
And performing a combined navigation experiment through vehicle-mounted experimental data according to the parameters to obtain attitude estimation errors, wherein the estimation errors of the course angles are mainly concerned in the experiment because the attitude estimation differences of the pitch angle and the roll angle are not large, and the estimation errors of the course angles of the three groups of experiments are respectively shown in figures 3-5. As can be seen, under the condition of three groups of large misalignment angles, SE (3) -Euler, SE (3) -Quat, SE (3) -RP and SE (3) -MRP can perform convergence of heading angle estimation errors, but the overall performance is comparatively better than that of SE (3) -Quat, SE (3) -RP and SE (3) -MRP. Furthermore, as the initial misalignment angle increases, the convergence takes longer, SE (3) -RP and SE (3) -MRP converge faster than SE (3) -Euler, and the final heading angle estimation errors SE (3) -RP and SE (3) -MRP are significantly smaller than SE (3) -Euler. Therefore, the Reed-Solomon strapdown inertial navigation error model based on the Rodrigue parameters and the Reed-Solomon strapdown inertial navigation error model based on the corrected Rodrigue parameters are superior to the traditional Reed-Solomon strapdown inertial navigation error model based on the Euler angle, and reflect the advantage of the rapid starting application of the Reed-Solomon strapdown inertial navigation error model based on the Rodrigue parameters and the Reed-Solomon strapdown inertial navigation error model based on the corrected Rodrigue parameters under the condition of a large misalignment angle.
So far, the technical solutions of the present invention have been described in connection with the preferred embodiments shown in the drawings, but it is apparent to those skilled in the art that the scope of the present invention is not limited to these specific embodiments. Equivalent changes or substitutions of related technical features can be made by those skilled in the art without departing from the principle of the invention, and the technical scheme after the changes or substitutions can fall into the protection scope of the invention.

Claims (1)

1. A Lee group strapdown inertial navigation error model unification based on a Rodrigues parameter is characterized by comprising the following steps: the method comprises the following steps of providing a lie group strapdown inertial navigation error model based on the Rodrigue parameters and corrected Rodrigue parameters, bringing the lie group strapdown inertial navigation error model based on the Euler angle, the quaternion, the Rodrigue parameters and the corrected Rodrigue parameters into a unified lie group strapdown inertial navigation error model, and comparing the advantages and disadvantages of the four models through experiments, wherein the method specifically comprises the following steps:
1) Analyzing the posture representation of the Rodrigues parameters, wherein the posture representation of the Rodrigues parameters is mainly divided into two types of posture estimation of the Rodrigues parameters and posture estimation of correction Rodrigues parameters;
2) Analyzing the lie group strapdown inertial navigation error model, simultaneously bringing the attitude error and the speed error into a group, and constructing a new lie group strapdown inertial navigation error model;
3) Deducing a Lei swarm strapdown inertial navigation error model based on the Rodrigue parameters and a Lei swarm strapdown inertial navigation error model based on the corrected Rodrigue parameters based on the definition of the Rodrigue parameters and the attitude errors of the corrected Rodrigue parameters;
4) According to the conversion relation among the Euler angle, the quaternion, the Rodrigues parameter and the corrected Rodrigues parameter, a unified Lei group strapdown inertial navigation error model is provided, and the four Lei group strapdown inertial navigation error models can be represented at the same time;
5) And (3) comparing the performances of the Liqun strapdown inertial navigation error model based on the Euler angle, the quaternion, the Rodrigue parameter and the corrected Rodrigue parameter through two groups of vehicle-mounted experiments.
CN202211080154.7A 2022-09-05 2022-09-05 Lei cluster strapdown inertial navigation error model unified formula based on Rodrigues parameters Pending CN115371706A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115727875A (en) * 2022-11-29 2023-03-03 哈尔滨理工大学 Non-singular transfer alignment method based on corrected Rodrigues parameters

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115727875A (en) * 2022-11-29 2023-03-03 哈尔滨理工大学 Non-singular transfer alignment method based on corrected Rodrigues parameters
CN115727875B (en) * 2022-11-29 2023-09-01 哈尔滨理工大学 Singular-free transfer alignment method based on modified Rodrigas parameter

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