CN103471614A - Transfer alignment method in polar region based on inverse coordinate system - Google Patents

Abstract

The invention discloses a transfer alignment method in a polar region based on an inverse coordinate system. The method comprises the steps of taking the earth as a sphere, converting carrier navigation information under the traditional coordinate system into the inverse coordinate system by establishing the inverse coordinate system, obtaining carrier navigation information under a new coordinate system, establishing a new geographic coordinate system based on the inverse coordinate system, establishing a state equation and a measurement equation of transfer alignment under the new coordinate system by establishing a quick velocity and posture transfer alignment matching method, establishing a Kalman filtering equation to estimate a misalignment angle of primary and secondary inertial navigation, and judging the feasibility of the transfer alignment in the polar region. The method solves the problem that the transfer alignment method based on the traditional geographic coordinate system cannot be used during navigation of a ship in the polar region. The method has the characteristics of independence, flexibility, simplicity and certain navigation accuracy, and is more applicable to launch of shipborne weapons in high latitudes and the polar region.

Description

Polar region transfer alignment method based on inverse coordinate system

Technical Field

The invention relates to a polar region transfer alignment method based on an inverse coordinate system, which can be used for launching ship-borne weapons of ships at high latitudes and in polar regions and energy survey navigation of ships in polar regions.

Background

The transfer alignment technology is one of initial alignment of a movable base, and the transfer alignment relates to two sets of inertial navigation systems. A set of high-precision inertial Navigation System is installed on both ships and airplanes, and is used as a main inertial Navigation System (MINS for short) of the ships and airplanes. The ship-borne weaponry and the airborne missile have own Inertial Navigation systems, generally, the accuracies of the Inertial Navigation systems are not very high, and the Inertial Navigation systems are called Slave Inertial Navigation Systems (SINS) compared with the master Inertial Navigation System. In the strap-down inertial navigation system, initial alignment is to determine an initial value of a strap-down matrix, and transfer alignment is to calibrate a misaligned sub inertial navigation system by using navigation information of a high-precision main inertial navigation system to determine an initial value of the strap-down matrix of the sub inertial navigation system.

Transfer alignment can be largely divided into two broad categories: calculating parameter matching and measuring parameter matching. Common matching methods are: the method comprises a speed matching method, a specific force matching method, an angular velocity matching method, an attitude matching method, a position matching method and the like, wherein the speed and position matching method is a mature transfer alignment matching method at present and is already applied to a plurality of weaponry. In addition, there are composite parameter matching methods such as: the method comprises a speed and angular velocity matching method, a speed and attitude matching method and the like, wherein the speed and attitude matching method is the highest matching method so far, and is also called as rapid transfer alignment.

Velocity plus pose matching transfer alignment is one of the fastest alignment methods to date. The speed and attitude matching utilizes the mixed parameter information for matching, and the observability of the system is improved. The speed and attitude matching transfer alignment combines the characteristics of speed error matching and attitude difference matching, and the alignment can be completed only by matching with the machine shaking action without long-time maneuvering of the transport carrier during the alignment. And the alignment time is short, and the attitude precision can reach below 1mrad within 10 seconds. Therefore, the speed plus pose matching transfer alignment is also called fast transfer alignment, and the application of fast transfer alignment in tactical weapons is more and more emphasized by researchers due to the short alignment time and high alignment accuracy. And speed and attitude matching transfer alignment introduces speed information on the basis of attitude matching, takes the speed error and the attitude difference of the main inertial navigation system and the sub inertial navigation system as observed quantities, and estimates the installation error angle between the main inertial navigation system and the sub inertial navigation system through Kalman filtering.

Polar region navigation is a technique for positioning and navigating a carrier near a polar region. When a ship navigates near a polar region, it is very difficult to locate the ship by applying the traditional longitude and latitude coordinate system. The longitude line in the polar region can be quickly converged, and the change rate of the longitude is very large when the ship navigates as an object, which requires that an overlarge control torque be applied to the azimuth gyroscope. When the ship navigates in the north and south directions, the course of the ship passes through the poles and can be changed by 180 degrees. So at the pole, the direction is meaningless. Navigation systems designed with the traditional latitude and longitude coordinate system cannot effectively work in high latitude areas. In order to overcome the problem that an inertial navigation system designed based on a traditional longitude and latitude coordinate system cannot work effectively, a free azimuth inertial navigation system and a free-moving azimuth inertial navigation system appear. But at calculated position and commanded angular rateWhile still having

Especially at the latitude

Near or equal to 90 deg., overfill overflow can occur for the computer, resulting in computer downtime. Therefore, the polar region navigation positioning needs to be solved, and the establishment of the coordinate system needs to be considered again.

Disclosure of Invention

The key problem to be solved by the invention is that when polar region navigation is carried out, a polar region transfer alignment method based on an inverse coordinate system is provided for the defect that the transfer alignment method under the traditional coordinate system can not carry out transfer alignment at high latitude and near the polar region, by establishing an inverse coordinate system, converting the basic navigation information under the traditional coordinate system into the inverse coordinate system, establishing a geographic coordinate system based on the inverse coordinate system, according to the traditional matching method of transfer alignment, a speed error differential equation of speed plus attitude matching alignment based on an inverse coordinate system and a misalignment angle differential equation of main and sub inertial navigation are deduced, so that when a ship navigates in a polar region, the method for transmitting and aligning based on the traditional geographic coordinate system is not applicable any more, and the feasibility of transmitting and aligning the ship navigation system at high latitude and near polar regions is greatly improved.

The technical scheme of the invention is as follows:

a polar region transfer alignment method based on an inverse coordinate system is characterized in that a new coordinate system, namely the inverse coordinate system, is established, a transfer alignment matching method of a traditional coordinate system is combined, a differential equation of velocity and attitude matching transfer alignment based on the inverse coordinate system is established, a state equation and a measurement equation of velocity and attitude matching are established, and a Kalman filtering method is utilized to obtain an estimated value of a misalignment angle between main inertial navigation and sub inertial navigation when a carrier sails near a polar region to carry out transfer alignment at high latitude. Firstly, a new geographic coordinate system based on an inverse coordinate system is established, high latitude and polar regions under a traditional coordinate system are converted into middle and low latitude regions under the inverse coordinate system, the position and course information of a carrier under the traditional coordinate system is converted into the inverse coordinate system by using the thought of mathematical geometry, the obtained related navigation information is used, a fast transfer alignment method of speed and attitude matching is used for deducing a polar region transfer alignment differential equation based on the inverse coordinate system, a differential equation of a speed error and a main and sub inertial navigation misalignment angle is established, a Kalman filtering model is established for carrying out filtering estimation on the misalignment angle of the main and sub inertial navigation, the problem that a ship can not carry out transfer alignment in the polar region is solved to a certain extent, and the precision of polar region transfer alignment is improved.

The method comprises the following specific steps:

(1) establishing an inverse coordinate system, and converting a traditional terrestrial coordinate system into the inverse coordinate system according to the coordinate conversion principle;

(2) establishing a new geographic coordinate system based on the inverse coordinate system;

(3) converting basic position information and course information of the carrier in a traditional terrestrial coordinate system into an inverse coordinate system, and obtaining longitude and latitude information and course information of the carrier in the inverse coordinate system through geometric operation;

(4) projecting the rotational angular velocity of the earth and the rotational angular velocity of the new geographic coordinate system to the new geographic coordinate system by using the established new geographic coordinate system;

(5) according to the steps (1) to (4), obtaining position information and course information of the carrier under an inverse coordinate system, and coordinate projection of the rotational angular velocity of the earth and the rotational angular velocity of the new geographic coordinate system in the new geographic coordinate system, and establishing a rapid transfer alignment differential equation based on the velocity and the attitude under the inverse coordinate system;

(6) and establishing a Kalman filtering model by using the established velocity plus attitude differential equation, and carrying out filtering estimation on the misalignment angle of the main inertial navigation and the sub inertial navigation.

The basic principle of the invention is as follows: converting high latitude and polar region under the traditional longitude and latitude coordinate system into middle and low latitude region under the definition of the inverse coordinate system by using the established inverse coordinate system, obtaining basic navigation information of a download body under the inverse coordinate system by converting navigation information between the two coordinate systems, as shown in figures 1 and 2, obtaining the rotation angular velocity of the earth and the projection coordinate of the navigation angular velocity of the carrier under the new geographic coordinate system by establishing a new geographic coordinate system based on the inverse coordinate system, as shown in figure 3, deducing a velocity error equation and a misalignment angle error equation based on the transmission alignment of the inverse coordinate system and the polar region by combining a matching method of transmission alignment under the traditional coordinate system, establishing a state equation model of transmission alignment by using a velocity and attitude matching method, and establishing a measurement equation of transmission alignment by using the velocity difference and attitude difference between main and sub inertial navigations as observed quantities, and finally, establishing a Kalman filtering model of velocity and attitude matching transfer alignment by utilizing a Kalman filtering method to realize filtering estimation of the actual misalignment angle between the main inertial navigation system and the sub inertial navigation system.

The invention has the advantages that: the method solves the defect that the ship-borne weapons cannot be effectively transferred and aligned at high latitudes and near polar regions in the traditional latitude and longitude coordinate system, designs a transfer and alignment scheme in an inverse coordinate system, utilizes a kinetic equation between navigation information and the main and sub inertial navigations to establish a transfer and alignment differential equation of polar region velocity and attitude matching, designs a Kalman filter of velocity and attitude matching, estimates a misalignment angle between the main and sub inertial navigations, solves the problem that the ship-borne weapons are seriously diverged to transfer and align at the high latitudes and near polar regions to influence the navigation precision, improves the application range of an inertial navigation system and the transfer and alignment precision of the ship-borne weapons in the high latitudes, and is more suitable for resource survey and strategic aerial view control of ships in the polar regions in China.

Drawings

FIG. 1 is a diagram of the position relationship of a carrier in a conventional coordinate system and an inverse coordinate system;

FIG. 2 is a heading relationship diagram between a conventional coordinate system and an inverse coordinate system;

FIG. 3 shows a new geographic coordinate system established under the inverse coordinate system;

FIG. 4 is a flow chart of the method of the present invention

Detailed Description

The present invention will be described in detail with reference to specific examples.

The method comprises the specific implementation procedures of firstly establishing an inverse coordinate system according to a coordinate transformation principle, then establishing a new geographic coordinate system based on the inverse coordinate system, obtaining navigation information under the inverse coordinate system by utilizing a coordinate relation of a carrier between the two coordinate systems and a spherical geometry principle, establishing a speed and attitude error differential equation of the main inertial navigation and the sub inertial navigation by utilizing the navigation information, then establishing a speed and attitude matching fast transfer alignment state equation and a measurement equation by utilizing the obtained differential equation, designing a filtering model of a Kalman filter, and estimating a misalignment angle between the main inertial navigation and the sub inertial navigation when the carrier is subjected to transfer alignment in a polar region.

The specific implementation steps are as follows:

1. information related to traditional latitude and longitude coordinate system

The earth model is assumed to be a sphere, the position coordinate of the carrier under the traditional coordinate system is P (x, y, z), and the longitude and latitude coordinate is P (x, y, z)

As shown in fig. 1.

Radius of the earth: r is 6378393.0m

Rotation angular velocity of the earth: 7.27220417e-5

2. Establishing an inverse coordinate system

The equatorial inertia system of the earth's center is unchanged, and the inverse coordinate system rotates the traditional longitude and latitude coordinate system XYZ through the coordinate axis principle and twice rotationTo obtain an inverse coordinate system

The first rotation is to rotate the polar axis Z under the traditional coordinate system around the X axis until the position of the Y axis of the traditional coordinate system to obtain the polar axis of the inverse coordinate systemRotating the Y axis of the traditional coordinate system to the X axis of the traditional coordinate system during the second rotation to obtain the position of the inverse coordinate system

Axis, obtaining an inverse coordinate system according to the right-hand coordinate system criterion

Wherein

The axis passes through the pole.

It is assumed here that the position coordinates of the carrier in the inverse coordinate system are

Longitude and latitude coordinates of

As shown in fig. 1.

3. Establishing a new geographic coordinate system based on an inverse coordinate system

As shown in FIG. 3, the new geographic coordinate system established at point P is the same plane as the conventional geographic coordinate system, except that the north direction is changed, and the geographic north of the new geographic coordinate system points to

4. Conversion of navigation information

(1) Longitude and latitude conversion under inverse coordinate system

The latitude and longitude information of the known carrier under the traditional coordinate system of the P point is

The position coordinates are (x, y, z); the longitude and latitude information of the P point of the carrier under the inverse coordinate system is assumed to be

The position coordinates are

The positions of the two coordinate systems of the carrier are shown in figure 1, and by utilizing the relationship between the longitude and latitude coordinates and the position coordinates and utilizing the position relationship between the inverse coordinate system and the traditional coordinate system, the longitude and latitude coordinates under the inverse coordinate system can be obtained as follows:

$\stackrel{-}{\mathrm{\λ}}=\arctan \left(\frac{x}{z}\right)---\left(2\right)$

(2) course information conversion

Because of the establishment of the inverse coordinate system, the polar axis changes, and the geographic north direction is not true north in the traditional true sense but points to the inverse coordinate system

The axis, here defined as positive in the counterclockwise direction, is shown in FIG. 2As shown, in the spherical triangular NPS, the course information of the carrier in the inverse coordinate system can be obtained by using the spherical geometry:

$\stackrel{\‾}{K}=K-P---\left(3\right)$

in the formula, P is the included angle of the meridian at the point P under the definition of two coordinate systems;

and K represents the course defined under the inverse coordinate system and the conventional coordinate system, respectively.

5. Projecting the rotational angular velocity of the earth and the rotational angular velocity of the new geographic coordinate system by using the established new geographic coordinate system

And moving to a new geographic coordinate system.

(1) Projection of angular velocity of rotation of the earth under a new geographic coordinate system

Establishing a geographic north orientation polar axis of a local horizontal geographic coordinate system based on an inverse coordinate system under the inverse coordinate system

As shown in fig. 3, therefore, the projection of the rotational angular velocity of the earth in the new geographic coordinate system can be derived from the relationship shown in fig. 3 as follows:

in the formula,

and

respectively, latitude and longitude defined in an inverse coordinate system.

(2) Projection of new geographic coordinate system rotation angular velocity

Assuming that the ship sailing speed is V, the solved course is utilizedThe projection of the velocity in the new geographic coordinate system can be derived as:

$V^{\stackrel{\‾}{t}}=\left[\begin{array}{c}{V}_x\\ V_y\end{array}\right]=\left[\begin{array}{c}V\sin \stackrel{\‾}{K}\\ V\cos \stackrel{\‾}{K}\end{array}\right]---\left(5\right)$

therefore, by utilizing the projection of the rotational angular velocity of the earth, the components of the rotational angular velocity of the new geographic coordinate system on each axis are obtained as follows:

in the formula, V_xAnd V_yRespectively representing the components of the carrier navigation speed in the horizontal direction; r is the mean radius of the earth.

6. Establishing polar region velocity and attitude matching transfer alignment differential equation

When an alignment error differential equation is transferred by velocity and attitude matching, in order to simplify calculation, the earth is set as a sphere, the influence of a lever arm effect and carrier deflection deformation is not considered, and an obtained error model is as follows:

$\left\{\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}^n=C_{\hat{s}}^n({[\mathrm{\φ}}_m\×]-[{\mathrm{\φ}}_a\×])f_m^s-(2{\mathrm{\Ω}}^n+{\mathrm{\ω}}_{\stackrel{\‾}{e}n}^n)\×{\mathrm{\δV}}^n+C_s^n{\widetilde{\▿}}^s\\ {\stackrel{\·}{\mathrm{\φ}}}_m=({\mathrm{\φ}}_m-{\mathrm{\φ}}_a)\×{\mathrm{\ω}}_{\mathrm{ns}}^s+{\widetilde{\mathrm{\ϵ}}}^s\\ {\stackrel{\·}{\mathrm{\φ}}}_a=0\end{array}\right.$

（7）

in the formula, phi_aThe actual installation error angle of the main inertial navigation unit is generally regarded as a fixed angle, and is assumed to be a constant value.

7. Establishing Kalman filtering model

Selecting a main and sub inertial navigation speed error delta V and a relative attitude misalignment angle phi_mAngle of sum and mounting error phi_aAs the state vector of the system, namely:

X＝[δV_x δV_y φ_mx φ_my φ_mz φ_ax φ_ay φ_az]^T

(1) establishment of equation of state

$\stackrel{\·}{X}=\mathrm{AX}+\mathrm{BW}$

Wherein,

$A=\left[\begin{array}{ccc}{A}_1& A_2& -{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="HDA0000371896600000011.png"\; state="\{\{state\}\}">A</figure-callout>}}_2\\ 0_{3\&times;3}& A_3& -A_3\\ 0_{3\&times;3}& 0_{3\&times;3}& 0_{3\&times;3}\end{array}\right],$

$A_2=\left[\begin{array}{ccc}{c}_{13}{f}_y-c_{12}{f}_z& -c_{13}{f}_x+c_{11}{f}_z& c_{12}{f}_x-c_{11}{f}_z\\ c_{23}{f}_y-c_{22}{f}_z& -c_{23}{f}_x+c_{21}{f}_z& c_{22}{f}_x-c_{21}{f}_z\end{array}\right]$ $A_3=\left[\begin{array}{ccc}0& {\mathrm{\&omega;}}_z& -{\mathrm{\&omega;}}_y\\ -{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA0000371896600000012.png"\; state="\{\{state\}\}">z</figure-callout>}}& 0& {\mathrm{\&omega;}}_x\\ {\mathrm{\&omega;}}_y& -{\mathrm{\&omega;}}_x& 0\end{array}\right]$

f^s＝[f_x f_y f_z]^T， ${\mathrm{\&omega;}}_{\mathrm{ns}}^s={\left[\begin{array}{ccc}{\mathrm{\&omega;}}_x& {\mathrm{\&omega;}}_y& {\mathrm{\&omega;}}_z\end{array}\right]}^T.$

$B=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000371896600000011.png"\; state="\{\{state\}\}">C</figure-callout>}}_{2\&times;2}& 0_{3\&times;3}& 0_{3\&times;3}\\ 0_{3\&times;2}& I_{3\&times;3}& 0_{3\&times;3}\\ 0_{3\&times;2}& 0_{3\&times;3}& I_{3\&times;3}\end{array}\right],$ $C_S^n=\left[\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right],$ ${\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000371896600000011.png"\; state="\{\{state\}\}">C</figure-callout>}}_{2\&times;2}=\left[\begin{array}{cc}{c}_{11}& c_{12}\\ c_{21}& {\mathrm{<figure-callout\; id="22"\; label="c"\; filenames="HDA0000371896600000012.png"\; state="\{\{state\}\}">c</figure-callout>}}_{22}\end{array}\right]$

calculation carrier coordinate system of representative sub-inertial navigation systemDirection cosine matrix to navigation coordinate system nCorresponding element, W is the system noise matrix.

(2) Establishment of measurement equation

By using a Kalman filtering model, a measurement equation of velocity plus attitude matching is as follows:

Z＝HX+v

wherein,

$H=\left[\begin{array}{ccc}{I}_{2\&times;2}& 0_{2\&times;3}& 0_{2\&times;3}\\ 0_{3\&times;2}& I_{3\&times;3}& 0_{3\&times;2}\end{array}\right]$

in the formula, $v={\left[\begin{array}{ccccc}{v}_{v\stackrel{\&OverBar;}{x}}& v_{v\stackrel{\&OverBar;}{y}}& v_{\mathrm{\&phi;m}\stackrel{\&OverBar;}{x}}& v_{\mathrm{\&phi;m}\stackrel{\&OverBar;}{y}}& v_{\mathrm{\&phi;mz}}\end{array}\right]}^T$ to measure a noise matrix.

And (3) integrating the state equation and the measurement equation established in the step (1) and the step (2), and finally obtaining the misalignment angle estimation value between the main inertial navigation and the sub inertial navigation by using a Kalman filtering method to finish transfer alignment.

Those skilled in the art will appreciate that the details of the present invention not described in detail herein are well within the skill of those in the art.

It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.

Claims (4)

1. A polar region transfer alignment method based on an inverse coordinate system is characterized by comprising the following steps:

(1) establishing an inverse coordinate system, and converting a traditional terrestrial coordinate system into the inverse coordinate system according to the coordinate conversion principle;

(2) establishing a new geographic coordinate system based on the inverse coordinate system;

(3) converting basic position information and course information of the carrier in a traditional terrestrial coordinate system into an inverse coordinate system, and obtaining longitude and latitude information and course information of the carrier in the inverse coordinate system through geometric operation;

(4) projecting the rotational angular velocity of the earth and the rotational angular velocity of the new geographic coordinate system to the new geographic coordinate system by using the established new geographic coordinate system;

(5) according to the steps (1) to (4), obtaining the position information and the course information of the carrier under the inverse coordinate system, and the coordinate projection of the rotational angular velocity of the earth and the rotational angular velocity of the new geographic coordinate system in the new geographic coordinate system, and establishing a rapid transfer alignment differential equation based on the velocity and the attitude under the inverse coordinate system;

(6) and establishing a Kalman filtering model by utilizing the established fast transfer alignment differential equation of the velocity and the attitude, and carrying out filtering estimation on the misalignment angle of the main inertial navigation and the sub inertial navigation.

2. The polar region transfer alignment method based on the inverse coordinate system as claimed in claim 1, wherein: and (3) converting the position and the course information of the carrier in the traditional coordinate system into new position and course information of the carrier in the inverse coordinate system.

3. The polar region transfer alignment method based on the inverse coordinate system as claimed in claim 1, wherein: projecting the rotational angular velocity of the earth and the rotational angular velocity of the new geographic coordinate system to the new geographic coordinate system in the step (4)

And obtaining the projection coordinates of the geographic coordinate system established by the two under the definition of the inverse coordinates.

4. The polar region transfer alignment method based on the inverse coordinate system as claimed in claim 1, wherein: in the step (5), the position and course information under an inverse coordinate system is obtained by converting the navigation information of the traditional coordinate system by using the carrier, and an error differential equation of speed and attitude matching transfer alignment is established by adopting a speed and attitude fast transfer matching method under the inverse coordinate system,

（1）

wherein,

wherein n is a navigation coordinate system (based on a geographic coordinate system under an inverse coordinate system); delta VⁿRepresents the speed error of the main inertial navigation and the sub inertial navigation in n system, delta V_xAnd δ V_yRespectively representing the speed error of the main inertial navigation and the sub inertial navigation in the horizontal direction based on the new geographic coordinate system;

representing a computational sub-inertial navigation coordinate system

An attitude direction cosine matrix to the n system; phi is a_mAnd phi₂Respectively representing the relative attitude angle error and the actual installation error angle between the main inertial navigation unit and the sub inertial navigation unit; [. radix Et rhizoma Rhei]Representing an anti-symmetric operation;

denotes n is relative to

Angular velocity of the system (inverse coordinate system);

representing the projection of the angular velocity of the sub inertial navigation coordinate system s relative to the n system under the s system;

specific force information output by the accelerometer;

and

respectively, accelerometer drift and gyro drift.

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