CN102052921B

CN102052921B - Method for determining initial heading of single-axis rotating strapdown inertial navigation system

Info

Publication number: CN102052921B
Application number: CN2010105508924A
Authority: CN
Inventors: 孙枫; 曹通; 高鹏; 高伟; 奔粤阳; 李举锋; 唐李军; 胡丹; 李国强; 曹冰
Original assignee: Harbin Engineering University
Current assignee: Harbin Engineering University
Priority date: 2010-11-19
Filing date: 2010-11-19
Publication date: 2012-08-22
Anticipated expiration: 2030-11-19
Also published as: CN102052921A

Abstract

The invention relates to a method for determining the initial heading of a single-axis rotating strapdown inertial navigation system, which comprises the steps of: 1 carrying out preheating preparation on the strapdown inertial navigation system; 2 determining an initial position parameter of a carrier by a global positioning system; 3 predetermining three attitudes of the carrier in position 1 and recording an output average value of a gyro in X direction and Y direction in position 1 within one minute; 4 collecting and recording an output average value of the gyro in X direction and Y direction in position 2 within one minute; 5 computing the constant drift epsilon x and epsilon y of the gyro in X direction and Y direction; 6 computing the precise azimuth aligning position of the strapdown inertial navigation system; and 7 estimating and compensating an azimuth misalignment angle by Kalman filtering to finish precise azimuth alignment. The existing single-axis rotating table is still used; and only the rotating table is controlled for putting an IMU (Inertial Measurement Unit) in a proper position for executing initial alignment so as to estimate the azimuth misalignment angle precisely, therefore, an initial heading angle is determined.

Description

method for determining initial course of single-axis rotation strapdown inertial navigation system

Technical Field

The invention relates to a measuring method. In particular to a method for determining the initial course of a strapdown inertial navigation system based on a single-axis rotary type optical fiber gyroscope.

Background

The rotary strapdown inertial navigation system is an autonomous and all-weather navigation system, and utilizes gyroscope and accelerometer to measure the linear motion and angular motion parameters of inertial unit (IMU) relative to inertial space, and under the condition of given initial condition, combines the angle value of IMU relative to carrier provided by rotating mechanism, and uses computer to make integral operation so as to continuously and real-timely provide position, speed and attitude information. It has the advantages of good concealment, no limitation of weather conditions and the like, and is widely applied to the fields of aviation, aerospace and navigation. The initial alignment error, especially the initial course error, is a main factor which causes the navigation precision of the strapdown inertial navigation system to be difficult to improve, and the influence of the initial course error on the system is shown not only on the measurement output of the carrier attitude, but also on the measurement of the speed and the position. Therefore, before the rotary strapdown inertial navigation system enters the navigation state, the initial heading of the carrier must be determined first.

For a ship strapdown inertial navigation system, the measurement precision of the initial attitude directly influences the navigation precision of the system. In the past, when Kalman filtering is used for initial alignment of a fixed position, an azimuth misalignment angle has certain estimation deviation due to unobservable ordinary drift of an east gyroscope, and further the measurement precision of an initial course is restricted.

Disclosure of Invention

The invention aims to provide a method for determining the initial course of a single-axis rotation strapdown inertial navigation system, which can eliminate the influence of constant drift of an east gyroscope on the estimation precision of an azimuth misalignment angle and improve the measurement precision of the initial course

The purpose of the invention is realized as follows:

step 1, preheating preparation is carried out on a strapdown inertial navigation system;

step 2, determining initial position parameters of the carrier through a Global Positioning System (GPS), and binding the initial position parameters into a navigation computer;

step 3, collecting the output of the fiber-optic gyroscope and the accelerometer assembly at the initial position of the ship, recording the output as the position 1, performing coarse alignment, and preliminarily determining three postures of the download body at the position: pitch angle theta₀Angle of inclination gamma₀And course angle

And recording the output average value of the X, Y directional gyroscope at the position within one minute

And 4, on the basis of the position 1, controlling the single-shaft rotary table to rotate 180 degrees around the azimuth rotating shaft to another position, recording the position as 2, collecting and recording the output average value of the X, Y-direction gyroscope in one minute on the position 2

Step 5, outputting the average value of the X, Y-direction gyroscope recorded according to the position 1

And X, Y-direction gyro output mean value recorded at position 2

Calculating the gyro constant drift epsilon in the direction of X, Y_x、ε_y；

Step 6, combining the initial attitude angle theta determined in the coarse alignment stage in the step 3₀、γ₀And

and the constant drift epsilon of the gyro in the X, Y direction obtained in the step 5_x、ε_yCalculating the accurate alignment position of the strapdown inertial navigation system and recording as a position 3;

and 7, controlling the single-axis turntable to rotate by an angle beta around the azimuth axis to a position 3 on the basis of the position 1, collecting the output of the fiber-optic gyroscope and the accelerometer component, establishing a Kalman filter state equation and a measurement equation by taking the speed error as an observed quantity, and estimating and compensating an azimuth misalignment angle by utilizing Kalman filtering to complete azimuth precise alignment.

The innovation of the present invention is step 5 and step 6, which will be described in more detail with respect to step 5 and step 6.

1. Calculating the gyro constant drift epsilon in the direction of X, Y_x、ε_yThe specific method comprises the following steps:

1) and acquiring and recording X, Y direction gyro output mean value at position 1

They are related to the constant drift of the gyro in the X, Y direction by

In the formula, ω_x、ω_yIs the true output value of the X, Y directional gyroscope;

2) collected and recorded X, Y at position 2Output mean value of directional gyroscope

They are related to the constant drift of the gyro in the X, Y direction by

(1) Adding the equation (2) to obtain a constant gyro drift epsilon in the direction of X, Y_x、ε_yIs composed of

2. The method for calculating the accurate azimuth alignment position of the strapdown inertial navigation system comprises the following steps:

the coordinate system of the northeast is taken as a navigation coordinate system, and a speed error equation and an attitude error equation of the strapdown inertial navigation system under the static base are expressed as

In the formula, omega_n＝ω_iecosL，Ω_u＝ω_iesinL，ω_ieIs the rotational angular velocity of the earth, L is the local geographical latitude, and is represented by phi in the formula (4-a)_nAnd phi in (4-c)_uMove to the left of the equation, respectively, to obtain

After the two-sided derivation of formula (5-b), the

Move to the left of the equation to obtain

Then the (5-a) and the (6) are substituted into the (5-b) to obtain

In the formula, V_n、

Are all directly measurable, i.e. the right front half of formula (7)

Are known; and epsilon_e、

For unmeasurable states, the azimuthal misalignment angle phi is estimated using Kalman filtering_uThe azimuth misalignment angle will have a steady state estimation error delta phi_u

Since the accelerometer accuracy is much higher than the gyroscope accuracy, i.e.

Therefore, the formula (8) is simplified to

An initial attitude matrix can be obtained by coarse alignment of the strapdown inertial navigation system

InitialI is an identity matrix, wherein b is a carrier matrixA label system; s is an IMU coordinate system; p is a calculated navigation coordinate system; for the conversion of the initial time between the s-system and the p-systemIs shown as

C_{s}^{p} (t_{0}) = C_{b}^{p} (t_{0}) C_{s}^{b} (t_{0})

Wherein the pitch angle theta₀Angle of inclination gamma₀And course angle

Three attitude angles obtained for coarse alignment;

after the single-shaft rotary type strapdown inertial navigation system rotates around the azimuth axis of the single-shaft rotary type strapdown inertial navigation system, the projection epsilon of the gyro constant drift under a navigation coordinate systemⁿIs composed of

Wherein, the IMU coordinate system s is converted into the navigation coordinate system n

Is shown as

C_{s}^{n} (t) = C_{p}^{n} (t) C_{s}^{p} (t) - - - (12)

In the formula

Phi (t) x is an antisymmetric matrix of the misalignment angle phi (t), and the formula (12) is substituted into the formula (11) to obtain

Neglecting the quadratic term error on the right side of the equation, equation (13) reduces to

Wherein,

C_{s}^{p} (t) = C_{b}^{p} (t_{0}) C_{s}^{b} (t)

beta is the angle of rotation of the turntable

Extending equation (14) and taking east projection epsilon of gyro constant drift_e

ε_e＝C₁₁ε_x+C₁₂ε_y+C₁₃ε_z (15)

Wherein,

at a pitch angle theta when the vessel is moored or at rest₀Angle of inclination gamma₀Are all small, and the attitude matrix element C₁₃Is not changed by the rotation of the IMU; thus, C₁₃Approximately zero, combining the formulas (9) and (15) to obtain

As can be seen from the formula (16), Δ φ_uOnly with the rotation angle β; therefore, if the azimuth misalignment angle estimation error Δ φ is made_uAt zero, the rotation angle β should satisfy the following relation

I.e. beta should satisfy

The rotation angle beta of the azimuth axis is obtained according to the formula (18), that is, the specific position of the position 3 is

<math> <mrow> <mi>β</mi> <mo>=</mo> <mi>arctan</mi> <mfrac> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>2</mn> </msub> </mfrac> <mo>+</mo> <mi>π</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow> </math>

In the formula,

the invention has the effective effect that the existing single-axis rotary table is continuously used, and the azimuth misalignment angle can be estimated with high precision only by controlling the rotary table to place the IMU at a proper position for initial alignment, so as to determine the initial course angle. The measuring technology is simple to operate. Compared with the prior fixed position initial alignment method, the technology greatly improves the measurement precision of the initial course on the premise of not reducing the initial alignment time, thereby improving the navigation performance of the fiber-optic gyroscope strapdown inertial navigation system.

In order to verify the effect of the initial course measurement technique, simulation was performed by Matlab software. The beneficial effects are shown in table one.

Watch 1

Azimuthal misalignment angle/(/) (^·)	Conventional methods	Improved method
			Set value	0.5000	0.5000
Estimated value	0.5613	0.5008
			Estimation accuracy	12.26％	1.60％

As can be seen from the table I, compared with the traditional method, the method has the advantages that the estimation accuracy reaches 1.60%, the high-accuracy initial course measurement is realized, and the navigation accuracy of the system is further improved.

The method starts from analyzing the east gyro constant drift, adjusts and controls the rotary table to place the IMU at a proper position, so that the projection component of the gyro constant drift in the navigation coordinate system can be automatically offset, the influence of the east gyro constant drift on the estimation precision of the azimuth misalignment angle is eliminated, and the measurement precision of the initial course is further improved.

Drawings

FIG. 1 is a single axis turntable orientation at position 1;

FIG. 2 is a single axis turret orientation at position 2;

FIG. 3 is a single axis turret orientation at position 3;

FIG. 4 is a comparison of the effect of the azimuthal misalignment angle estimation of the conventional method and the improved method;

FIG. 5 is a flow chart of an initial heading measurement technique.

Detailed Description

Step 1, preheating preparation is carried out on the strapdown inertial navigation system, and specific preheating time is set according to the requirements of the system.

And 2, determining initial position parameters of the carrier through a Global Positioning System (GPS), and binding the initial position parameters into a navigation computer.

And 3, after preheating, acquiring the output of the fiber-optic gyroscope and the accelerometer assembly at the initial position (recorded as position 1) of the ship, adjusting the strapdown inertial navigation system to complete the coarse alignment task of initial alignment, and preliminarily determining three attitude angles of the carrier at the position: pitch angle theta₀Angle of inclination gamma₀And course angle

And 4, controlling the single-shaft rotary table to rotate 180 degrees around the azimuth rotating shaft to another position on the basis of the position 1, and recording the position as a position 2. Average output from X, Y gyros was collected and recorded at position 2 over a one minute period

And X, Y-direction gyro output mean value recorded at position 2

Calculating the gyro constant drift epsilon in the direction of X, Y_x、ε_y。

and the constant drift epsilon of the gyro in the X, Y direction obtained in the step 5_x、ε_yAnd calculating the position of the strapdown inertial navigation system, and recording the position as 3.

And 7, controlling the single-shaft rotary table to rotate around the azimuth axis by an angle beta to a position 3 on the basis of the position 1. Collecting the output of the fiber-optic gyroscope and the accelerometer component, establishing a Kalman filter state equation and a measurement equation by taking the speed error as an observed quantity, and estimating and compensating an azimuth misalignment angle by utilizing Kalman filtering to complete an azimuth precise alignment task.

The invention also has the following features:

1. the specific features of step 5 are described below

They are related to the constant drift of the gyro in the X, Y direction by

In the formula, ω_x、ω_yIs the true output value of the X, Y directional gyroscope.

2) And collecting and recording X, Y direction gyro output average value at position 2

They are related to the constant drift of the gyro in the X, Y direction by

(20) When the equation (21) is added to the equation (a), the gyro constant shifts ε in the X, Y direction_x、ε_yCan be expressed as

2. The specific features of step 6 are described below:

an initial attitude matrix can be obtained by coarse alignment of the strapdown inertial navigation systemInitial

(I is an identity matrix). Wherein, b is a carrier coordinate system; s is an IMU coordinate system; p is a calculated navigation coordinate system; for the conversion of the initial time between the s-system and the p-system

Is shown as

C_{s}^{p} (t_{0}) = C_{b}^{p} (t_{0}) C_{s}^{b} (t_{0})

Wherein the pitch angle theta₀Angle of inclination gamma₀And course angle

Three attitude angles obtained for coarse alignment.

The rotation angle β of the azimuth axis can be obtained from the expressions (22) and (23), that is, the specific position of the position 3 is

<math> <mrow> <mi>β</mi> <mo>=</mo> <mi>arctan</mi> <mfrac> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>2</mn> </msub> </mfrac> <mo>+</mo> <mi>π</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>24</mn> <mo>)</mo> </mrow> </mrow> </math>

In the formula,

Claims

1. A method for determining an initial course of a single-axis rotating strapdown inertial navigation system is characterized by comprising the following steps:

step 2, determining initial position parameters of the carrier through a global positioning system, and binding the initial position parameters into a navigation computer;

And X, Y-direction gyro output mean value recorded at position 2

step 7, on the basis of the position 1, controlling the single-shaft turntable to rotate around the azimuth axis by an angle beta to a position 3,

<math> <mrow> <mi>β</mi> <mo>=</mo> <mi>arctan</mi> <mfrac> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>2</mn> </msub> </mfrac> <mo>+</mo> <mi>π</mi> <mo>,</mo> </mrow> </math>

collecting the output of the fiber-optic gyroscope and the accelerometer component, establishing a Kalman filter state equation and a measurement equation by taking the speed error as an observed quantity, and estimating and compensating an azimuth misalignment angle by utilizing Kalman filtering to complete azimuth precise alignment.

2. According to the claimsSolving 1 the method for determining the initial course of the single-axis rotation strapdown inertial navigation system is characterized by comprising the following steps: the gyro constant drift epsilon in the X, Y direction is calculated_x、ε_yThe specific method comprises the following steps:

(1) and acquiring and recording X, Y direction gyro output mean value at position 1

They are related to the constant drift of the gyro in the X, Y direction by

In the formula, ω_x、ω_yIs the output true value of the X, Y directional gyroscope；

(2) And collecting and recording X, Y direction gyro output average value at position 2They are related to the constant drift of the gyro in the X, Y direction by

3. The method for determining the initial heading of the single-axis rotating strapdown inertial navigation system as claimed in claim 2, wherein: the method for calculating the accurate azimuth alignment position of the strapdown inertial navigation system comprises the following steps:

In the formula, omega_n＝ω_ie cos L，Ω_u＝ω_ie sin L，ω_ieIs the rotational angular velocity of the earth, L is the local geographical latitude, will (4-a)

In the formula_nAnd phi in (4-c)_uMove to the left of the equation, respectively, to obtain

After the two-sided derivation of formula (5-b), the

Move to the left of the equation to obtain

Then the (5-a) and the (6) are substituted into the (5-b) to obtain

In the formula, V_n、

Are all directly measurable, i.e. the right front half of formula (7)

Are known; and epsilon_e、For unmeasurable states, the azimuthal misalignment angle phi is estimated using Kalman filtering_uThe azimuth misalignment angle will have a steady state estimation error delta phi_u

Therefore, the formula (8) is simplified to

Initial

I is a unit matrix, wherein b is a carrier coordinate system; s is an IMU coordinate system; p is a calculated navigation coordinate system; for the conversion of the initial time between the s-system and the p-systemIs shown as

C_{s}^{p} (t_{0}) = C_{b}^{p} (t_{0}) C_{s}^{b} (t_{0})

Wherein the pitch angle theta₀Angle of inclination gamma₀And course angle

Three attitude angles obtained for coarse alignment;

Is shown as

C_{s}^{n} (t) = C_{p}^{n} (t) C_{s}^{p} (t) - - - (12)

In the formula

Wherein,

C_{s}^{p} (t) = C_{b}^{p} (t_{0}) C_{s}^{b} (t)

beta is the angle of rotation of the turntable

ε_e＝C₁₁ε_x+C₁₂ε_y+C₁₃ε_z (15)

Wherein,

I.e. beta should satisfy

In the formula,