阅读说明：本技术 一种基于单光纤陀螺的高精度四位置寻北方法 (High-precision four-position north-seeking method based on single fiber gyroscope ) 是由 褚洋杨 张跃东 郭英然 李海森 徐文超 王志敏 黄建招 吴红 刘希亮 陈河 李振 于 2020-07-06 设计创作，主要内容包括：本发明属于单光纤陀螺寻北技术领域,涉及一种基于单光纤陀螺的高精度四位置寻北方法。本发明针对光纤陀螺随机游走系数大的特点,根据初始方位角的不同,合理分配各位置采样时间,改进了四位置寻北方案,在相同陀螺精度和采样总时间的条件下,进一步提高四位置寻北的精度。(The invention belongs to the technical field of single fiber gyroscope north finding, and relates to a high-precision four-position north finding method based on a single fiber gyroscope. Aiming at the characteristic of large random walk coefficient of the fiber-optic gyroscope, the invention reasonably distributes sampling time of each position according to different initial azimuth angles, improves the four-position north-seeking scheme, and further improves the precision of the four-position north-seeking under the condition of the same gyroscope precision and total sampling time.)

1. A high-precision four-position north-seeking method based on a single fiber gyroscope is characterized by comprising the following steps:

step 1, north-seeking formula

step 2, obtaining error propagation coefficients of different positions according to the formula (1) to obtain a north-seeking variance caused by gyro random walk, wherein the north-seeking variance is as follows:

wherein the content of the first and second substances,

step 3, recording

The extreme point is satisfied

Can find the extreme point

Step 4, adding a compass on the traditional single fiber gyro north seeker, and obtaining an azimuth angle according to the compass by roughly seeking north

2. The high-precision four-position north-seeking method based on the single fiber gyroscope as claimed in claim 1, wherein the four-position north-seeking formula in step 4 is

Wherein D ═ K ω + D₀D is the output of the gyro, K is the scale factor of the gyro, omega is the angular velocity sensed by the gyro, D₀Zero bias for the gyro, random error;

neglecting random errors, then have

Technical Field

The invention belongs to the technical field of single fiber gyroscope north finding, and relates to a high-precision four-position north finding method based on a single fiber gyroscope.

Background

The north finder operates under the condition that the carrier is static, and when the sensitive axis of the gyro is static in the horizontal plane of the ground, the sensed angular speed is only equal to the rotational angular speed omega of the earth_ieNorth component ω in the horizontal plane_NAnd azimuth angleIs related to the size of the cell. As shown in fig. 1 and 2, N indicates the north direction, and U indicates the sky direction. L refers to the local latitude. When gyro sensitive axis Y_gThe angle between the magnetic field and the true north isAt an angular velocity ω measured by the gyro of

In static north seeking, the gyroscope rotates along with the rotating shaft to be positioned to different sampling points and then is static to acquire data, and north seeking calculation is performed after all data acquisition is completed. Common static north-seeking schemes are divided into two-position, four-position, and multi-position north-seeking depending on how many sampling positions are.

Constant drift such as zero offset can be eliminated in north-seeking solution through subtraction of sampling data at different positions. Firstly, acquiring gyroscope data at an initial position, then driving the gyroscope to rotate by a rotating shaft, positioning to different sampling positions by a photoelectric encoder to acquire data, and finally performing corresponding north seeking and resolving. The angular velocity omega measured by the fiber-optic gyroscope at different rotation points is

Wherein the content of the first and second substances,at the initial azimuth, α is the angle at which the indexing mechanism rotates the gyroscope.

As shown in fig. 3, in the conventional four-position north-seeking, positions at 90 ° intervals in sequence are selected in a circle to acquire gyro output data at equal sampling times. After the gyroscope data acquisition is finished at the initial position, the fiber optic gyroscope sequentially rotates to other three sampling positions through the indexing mechanism to acquire data, and then the fiber optic gyroscope is positioned at four positions (P)₁、P₂、P₃、P₄) Sensed rotational angular velocity omega of the earth₁、ω₂、ω₃、ω₄Components are respectively

Can find an azimuth angle of

Formula from north seekingThe azimuth angle information can be solved by only acquiring data of the fiber-optic gyroscope at four positions, and the latitude and the fiber-optic gyroscope are not neededHelical scale factors, etc. The performance of the gyroscope is the most key factor influencing the north-seeking accuracy, the north-seeking system focuses on the accuracy and the rapidity, but the accuracy and the rapidity are mutually restricted, and the north-seeking accuracy is generally improved along with the increase of north-seeking time.

The optical fiber gyroscope has larger white noise due to the characteristics of optical elements of the optical fiber gyroscope, and the white noise is integrated in a certain time to cause angular random walk, so that the random walk coefficient is a very important index for the optical fiber gyroscope, and reflects the angular rate white noise output by the gyroscope.

According to the characteristics of white noise, the mean square error of angular rate measurement is related to the average time, and the generally defined zero-bias stability has no way to reflect the noise magnitude, so that the angular rate variance is normalized with the detection bandwidth to express the noise magnitude. I.e. mean square error of gyro output angular rate sigma_ΩDivided by the corresponding bandwidth B_eThe square root of (A) is defined as the random walk coefficient RWC, i.e.

When the detection bandwidths are different, although the obtained zero offset stability is different, the random walk coefficients are not changed, the larger the index is, the faster the mean square error of the random walk increases along with the time, and the larger the corresponding white noise is.

The root mean square of the gyro angular rates measured at different sampling frequencies are therefore different. The angular rate white noise increases with the increase of the measurement bandwidth, and the accurate measurement of the white noise indicates the detection bandwidth. The random walk coefficient can be regarded as the root mean square of the angular rate under a unit bandwidth, is independent of the detection bandwidth, and is an important parameter for measuring the noise level.

When only angular rate white noise exists, the white noise output by the method is the product of the random walk coefficient RWC and the square root of the detection bandwidth, namely the ratio of the random walk coefficient RWC to the square root of the sampling time t:

it can be seen that the longer the sampling time is, the smaller the obtained gyro angular rate noise is, and the accuracy and the rapidity are mutually restricted.

Therefore, how to achieve a balance between sampling time and north-seeking accuracy is the key to improve the fast north-seeking accuracy. No specific solution is disclosed at present.

Disclosure of Invention

In order to achieve the purpose, the invention provides a high-precision four-position north-seeking method based on a single fiber gyroscope, which reasonably distributes sampling time of each position according to different initial azimuth angles to improve a four-position north-seeking scheme, and achieves the purpose of further improving the four-position north-seeking precision under the condition of the same gyroscope precision and total sampling time.

The technical scheme is as follows: a high-precision four-position north-seeking method based on a single fiber gyroscope comprises the following steps:

step 1, north-seeking formulaThe angular velocity error transfer coefficients of each position obtained by partial differentiation are respectively:

step 2, obtaining error propagation coefficients of different positions according to the formula (1) to obtain a north-seeking variance caused by gyro random walk, wherein the north-seeking variance is as follows:

wherein the content of the first and second substances,a fixed value for a particular gyro;

step 3, recordingWhen the total time is T, the calculation is performed under the condition T₁+t₂+t₃+t₄Under T f (T)₁,t₂,t₃,t₄) Minimum value of (A), then

The extreme point is satisfied

Can find the extreme point

Step 4, adding a compass on the traditional single fiber gyro north seeker, and obtaining an azimuth angle according to the compass by roughly seeking north

And the total sampling time T is required, and after sampling is carried out by distributing the sampling time of four positions according to the formula (3), north seeking calculation is carried out by utilizing a four-position north seeking formula.

The four-position north-seeking formula in the step 4 is as follows

Wherein D ═ K ω + D₀D is the output of the gyro, K is the scale factor of the gyro, omega is the angular velocity sensed by the gyro, D₀Zero bias for the gyro, random error;

neglecting random errors, then have

According to the invention, after the data sampling time of four positions is distributed according to the requirement of the total north-seeking time T, the north-seeking data is acquired and solved, so that the north-seeking precision can be improved.

Take the case that the sampling time is equal at each position, i.e.

The method comprises the following steps:

a single-gyroscope four-position north-seeking method of the traditional method is to conduct north-seeking calculation after four positions at intervals of 90 degrees are sampled at equal time.

The method of the invention carries out north seeking after the sampling time distribution by using the formula (3), and takes the initial azimuth angle as 20 degrees as an example, the sampling time is distributed as t according to the improved four-position north seeking method₁＝t₃＝0.1334T、t₂＝t₄0.3666T, the north-seeking scheme is improvedThereby reducing north-seeking errors caused by random walks.

Has the advantages that:

the invention improves the north-seeking method by analyzing the influence of random walk on the single-gyroscope four-position north-seeking error, reasonably distributes sampling time of each position after obtaining the rough azimuth angle of the initial position by utilizing the output data of the compass or the gyroscope at a single position, improves the four-position north-seeking scheme, and further improves the four-position north-seeking precision under the condition of the same gyroscope precision and total sampling time.

Drawings

FIG. 1 shows the rotational angular velocity ω of the earth_ieA component map in a geographic coordinate system;

FIG. 2 is a schematic view of the direction of the sensitive axis of the gyroscope;

FIG. 3 is a four-position north-seeking indexing schematic;

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

Detailed Description

Because the north-seeking time is short, the zero offset change in a short period is small, and the zero offset change can be ignored relative to the random walk coefficient RWC, only the influence of the random walk coefficient RWC on the measurement angular velocity is considered:

t is the sampling time

Therefore, when the sampling time t is different, the measurement accuracy is different, and the angular velocity error caused by random walk is different for each measurement positionComprises the following steps:

as shown in FIG. 4, step 1, the formula of north finding

Partial differentiation is carried out to obtain angular velocity error transfer coefficients of all positions;

step 2, solving error propagation coefficients of different positions according to the formula to obtain a north-seeking variance caused by random walk of the gyroscope, wherein the north-seeking variance is as follows:

wherein the content of the first and second substances,for a particular top isFixed value obtained by Lagrange methodThe minimum extreme point of the optical fiber gyroscope can ensure that the north-seeking error caused by the random walk of the optical fiber gyroscope is minimum by reasonably distributing the sampling time.

Step 3, recording

When the total time is T, the calculation is performed under the condition T₁+t₂+t₃+t₄Under T f (T)₁,t₂,t₃,t₄) Minimum value of (1), record

The extreme point is satisfied

Can find the extreme point

It can be seen that the first and third position sampling times are highly accurate when the azimuth is near the east-west direction, and the second and fourth position sampling times are highly accurate when the azimuth is near the north-south direction.

When the azimuth angle is 45 degrees, the angle is changed,the time precision is higher.

Step 4, carrying out rough north finding by utilizing compass or single-position gyroscope output data to obtain approximate azimuth angleThen using the formula

And the total time T of north seeking is required to distribute the data sampling time of the four positions, and then the north seeking data is acquired and solved, so that the north seeking precision can be improved theoretically.

Take the case that the sampling time is equal at each position, i.e.

The method comprises the following steps:

a single-gyroscope four-position north-seeking method of the traditional method is to conduct north-seeking calculation after four positions at intervals of 90 degrees are sampled at equal time.

The improved north-seeking method is characterized in that the improved north-seeking method is implemented by analyzing the influence of random walk on single-gyroscope four-position north-seeking errors, the improved north-seeking method is implemented by acquiring a rough azimuth angle of an initial position by utilizing compass or gyroscope output data of a single position, distributing sampling time by utilizing a formula (3), and then seeking north, and taking the initial azimuth angle as 20 degrees as an example, distributing the sampling time as t according to the improved four-position north-seeking method₁＝t₃＝0.1334T、t₂＝t₄0.3666T, the north-seeking scheme is improved

Thereby reducing north-seeking errors caused by random walks.

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.