CN107167134A - Redundant configuration laser gyro navigation inertial navigation co-located method - Google Patents

Redundant configuration laser gyro navigation inertial navigation co-located method Download PDF

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CN107167134A
CN107167134A CN201710477808.2A CN201710477808A CN107167134A CN 107167134 A CN107167134 A CN 107167134A CN 201710477808 A CN201710477808 A CN 201710477808A CN 107167134 A CN107167134 A CN 107167134A
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CN107167134B (en
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吴文启
王林
曹聚亮
练军想
铁俊波
潘献飞
何晓峰
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National University of Defense Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
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Abstract

The problem of present invention between redundant configuration laser gyro navigation inertial navigation system for lacking information fusion and effective co-located method, disclose redundant configuration laser gyro navigation inertial navigation co-located method.The present invention modulates the steps such as laser gyro navigation inertial navigation relative performance online evaluation, single-shaft-rotation modulation laser gyro navigation inertial navigation ascertainment error predictive compensation by joint error state Kalman filtering, system noise impact analysis, dual-axis rotation, realize without under the conditions of extraneous reference information, the online evaluation of relative performance between two sets of dual-axis rotations modulation laser gyro navigation inertial navigation of redundant configuration, while improving the positioning precision of the single-shaft-rotation modulation laser gyro navigation inertial navigation of redundant configuration.The present invention is significant available for the information fusion between redundant configuration laser gyro navigation inertial navigation under the high-precision guidanuce condition of long endurance for improving the survival ability under naval vessels severe sea condition environment.

Description

Redundant configuration laser gyro navigation inertial navigation cooperative positioning method
Technical Field
The invention relates to a laser gyro navigation inertial navigation positioning method, in particular to a redundant configuration laser gyro navigation inertial navigation cooperative positioning method, and belongs to the field of inertial navigation.
Background
The rotary modulation laser gyro navigation inertial navigation realizes the compensation of the deterministic error of an inertial device by means of a rotary mechanism, so that the precision of the inertial navigation is improved, and the researchers at home and abroad develop extensive research on the method so as to meet the requirements of various naval vessels on long-endurance high-precision navigation and positioning. In the north country represented by the united states, various naval vessels of the navy are generally provided with single-axis rotation modulation laser gyro navigation inertial navigation and double-axis rotation modulation laser gyro navigation inertial navigation, and the main representative products are as follows: MK39 series, MK49 series, AN/WSN-7 series. The single-axis rotation modulation laser gyro navigation inertial navigation system generally rotates around an azimuth axis periodically, can modulate the influence of gyro drift in a horizontal direction and zero offset of an accelerometer on navigation positioning, but cannot modulate the influence of the azimuth gyro drift, and can cause deterministic positioning error in direct proportion to navigation time; the biaxial rotation modulation laser gyro navigation inertial navigation system generally rotates around an azimuth axis and a roll axis periodically, the influence of the drift of three laser gyros and the zero offset of an accelerometer on navigation positioning can be modulated, and the main factor influencing the positioning precision of the biaxial rotation modulation laser gyro navigation inertial navigation system is random error caused by random angular wandering of the laser gyro, which can cause positioning error in direct proportion to the square root of navigation time.
In consideration of reliability, a plurality of sets of inertial navigation systems are generally configured in a redundant manner for various vessels, and typically, a set of single-axis rotation modulation laser gyro navigation inertial navigation system and two sets of double-axis rotation modulation laser gyro navigation inertial navigation systems are configured in a redundant manner. Compared with the single-axis rotation modulation laser gyro navigation inertial navigation, the double-axis rotation modulation laser gyro navigation inertial navigation can provide a higher-precision positioning result, but the structure is complex, the manufacturing cost is higher, and the failure rate is higher than that of the single-axis rotation modulation laser gyro navigation inertial navigation. Under the condition of redundant configuration of the laser gyro navigation inertial navigation, one set of the double-shaft rotation modulation laser gyro navigation inertial navigation system is generally used as a main inertial navigation system, the rest set of the double-shaft rotation modulation laser gyro navigation inertial navigation system and the single-shaft rotation modulation laser gyro navigation inertial navigation system are only used as hot backup systems, information fusion is lacked among the three sets of systems, and an effective cooperative positioning method is lacked.
When no external reference information exists, an inertial navigation system with better performance (smaller random error) is preferably selected from the two sets of biaxial rotation modulation laser gyro navigation inertial navigation systems, and an effective evaluation method is lacked, so that the performance quality between the two sets of biaxial rotation modulation laser gyro navigation inertial navigation systems in an actual working environment cannot be guaranteed to be consistent with experience selection; in view of the relatively higher failure rate of the biaxial rotation modulation laser gyro navigation inertial navigation, the uniaxial rotation modulation laser gyro navigation inertial navigation is usually used as a final navigation positioning guarantee system, but because the influence of azimuth gyro drift cannot be modulated, the azimuth gyro drift can cause a deterministic positioning error in direct proportion to navigation time, and under the condition of ensuring the reliability of naval vessel navigation positioning, the improvement of the positioning accuracy of the uniaxial rotation modulation laser gyro navigation inertial navigation as a final safety defense line of naval vessel navigation positioning has extremely important significance.
Therefore, the solution for realizing the key point of the cooperative positioning through the information fusion between the inertial navigation systems needs to be provided: 1. and (2) preferably selecting an inertial navigation system with better performance (smaller random error) from the two sets of biaxial rotation modulation laser gyro navigation inertial navigation systems as a main inertial navigation system, and ensuring to obtain an optimal navigation positioning result 2. carrying out prediction compensation on deterministic positioning error which is directly proportional to navigation time and is caused by the drift of a uniaxial rotation modulation laser gyro navigation inertial navigation azimuth gyro, so that the positioning accuracy is improved, and even if the two sets of biaxial rotation modulation laser gyro navigation inertial navigation systems simultaneously have an extreme condition of failure, the uniaxial rotation modulation laser gyro navigation inertial navigation system which compensates the deterministic positioning error can also provide high-accuracy positioning.
Disclosure of Invention
The invention provides a redundant configuration laser gyro navigation inertial navigation cooperative positioning method, which aims at solving the problem that redundant configuration laser gyro navigation inertial navigation systems lack an information fusion and effective cooperative positioning method. The method respectively establishes a joint error state equation of the single-axis rotation modulation laser gyro navigation inertial navigation and two sets of double-axis rotation modulation laser gyro navigation inertial navigation, and estimates the joint error state through Kalman filtering by taking the speed and position difference value between the single-axis rotation modulation laser gyro navigation inertial navigation and the double-axis rotation modulation laser gyro navigation inertial navigation inertial navigation after deducting a lever arm effect as an observed quantity. Because the biaxial rotation modulation laser gyro navigation inertial navigation system generally rotates around the azimuth axis and the roll axis periodically, the influence of the drift of three laser gyros and the zero offset of an accelerometer on navigation positioning can be modulated, and the main factor influencing the positioning precision of the biaxial rotation modulation laser gyro navigation inertial navigation system is random error caused by random angular wandering of the laser gyro, which can cause positioning error in direct proportion to the square root of navigation time. Therefore, the speed and position difference between the single-axis rotation modulation laser gyro navigation inertial navigation and the double-axis rotation modulation laser gyro navigation inertial navigation is taken as an observed quantity, the azimuth gyro drift uncertainty of the single-axis rotation inertial navigation obtained by the joint error state Kalman filtering estimation of the double-axis rotation modulation laser gyro navigation inertial navigation with large random error and the single-axis rotation modulation laser gyro navigation inertial navigation is larger, the on-line evaluation of the relative performance between two sets of double-axis rotation modulation laser gyro navigation inertial navigation can be realized by taking the azimuth gyro drift uncertainty as an evaluation index, and the double-axis rotation modulation laser gyro navigation inertial navigation with smaller random error is preferably selected as a main inertial navigation system without external reference information; the double-axis rotation modulation laser gyro navigation inertial navigation with small random error and the single-axis rotation modulation laser gyro navigation inertial navigation have smaller uncertainty of azimuth gyro drift of the single-axis rotation modulation laser gyro navigation inertial navigation obtained by united error state Kalman filtering estimation, higher estimation precision, further prediction compensation is carried out on deterministic positioning error related to the azimuth gyro drift estimation value, and the positioning precision of the single-axis rotation modulation laser gyro navigation inertial navigation as the last safety defense line of naval vessel navigation positioning is improved. The method for redundantly configuring the laser gyro navigation inertial navigation cooperative positioning solves the problem of information fusion among inertial navigation systems under the condition of no external reference information, maximizes information utilization, and has great significance for improving the survival capability of the naval vessel under severe sea condition.
The technical solution adopted for realizing the invention is as follows:
a laser gyro navigation inertial navigation cooperative positioning method with redundant configuration comprises the following steps:
the method comprises the following steps: respectively determining the joint error states between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 2, the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 3, wherein the joint error states are respectively
x12(t)＝[φE12φN12φU12vE12vN12L12λ12 x1 y1 z1 x2 y2 z2▽x1▽y1▽x2▽y2]T(1)
x13(t)＝[φE13φN13φU13vE13vN13L13λ13 x1 y1 z1 x3 y3 z3▽x1▽y1▽x3▽y3]T(2)
Wherein x is12(t) is the combined error state between the single-axis rotation modulation laser gyro navigation inertial navigation 1 and the double-axis rotation modulation laser gyro navigation inertial navigation 2, x13(t) is the combined error state phi between the single-axis rotation modulation laser gyro navigation inertial navigation 1 and the double-axis rotation modulation laser gyro navigation inertial navigation 3E12＝φE1-φE2Modulating laser gyro navigation inertial navigation 1 east attitude error phi for single axis rotationE1Laser gyro navigation inertial navigation 2 east attitude error phi modulated by double-axis rotationE2Difference of (phi)N12＝φN1-φN2Modulating laser gyro navigation inertial navigation 1 north attitude error phi for single axis rotationN1And biaxial rotation modulation laser gyro navigation inertial navigation 2 north attitude error phiN2Difference of (phi)U12＝φU1-φU21-day attitude error phi of laser gyro navigation inertial navigation modulated by single-axis rotationU1And the biaxial rotation modulation laser gyro navigation inertial navigation 2-day attitude error phiU2Difference of (phi)E13＝φE1-φE3Modulating laser gyro navigation inertial navigation 1 east attitude error phi for single axis rotationE1Laser gyro navigation inertial navigation 3 east attitude error phi modulated by double-axis rotationE3Difference of (phi)N13＝φN1-φN3Modulating laser gyro navigation inertial navigation 1 north attitude error phi for single axis rotationN1And the double-shaft rotation modulation laser gyro navigation inertial navigation 3 north attitude error phiN3Difference of (phi)U13＝φU1-φU31-day attitude error phi of laser gyro navigation inertial navigation modulated by single-axis rotationU13-day attitude error phi of laser gyro navigation inertial navigation modulated by double-axis rotationU3Difference of vE12＝vE1-vE2Modulating laser gyro navigation inertial navigation 1 east direction velocity error v for single axis rotationE1And biaxial rotation modulation laser gyro navigation inertial navigation 2 east direction velocity error vE2Difference of vN12＝vN1-vN2Modulating laser gyro navigation inertial navigation 1 north velocity error v for single axis rotationN1And biaxial rotation modulation laser gyro navigation inertial navigation 2 north direction velocity error vN2Difference of vE13＝vE1-vE3Modulating laser gyro navigation inertial navigation 1 east direction velocity error v for single axis rotationE1And biaxial rotation modulation laser gyro navigation inertial navigation 3 east direction velocity error vE3Difference of vN13＝vN1-vN3Modulating laser gyro navigation inertial navigation 1 north direction speed for single axis rotationError vN1And biaxial rotation modulation laser gyro navigation inertial navigation 3 north direction velocity error vN3Difference of (D), L12＝L1-L2Method for modulating 1 latitude error L of laser gyro navigation inertial navigation for single-axis rotation12-latitude error L of navigation inertial navigation of laser gyro modulated by double-axis rotation2A difference of (a)12＝λ1-λ2Method for modulating 1 longitude error lambda of laser gyro navigation inertial navigation for single-axis rotation1Laser gyro navigation inertial navigation 2 longitude error lambda modulated by double-axis rotation2Difference of (D), L13＝L1-L3Method for modulating 1 latitude error L of laser gyro navigation inertial navigation for single-axis rotation1Laser gyro navigation inertial navigation 3 latitude error L modulated by double-shaft rotation3A difference of (a)13＝λ1-λ3Method for modulating 1 longitude error lambda of laser gyro navigation inertial navigation for single-axis rotation1Laser gyro navigation inertial navigation 3 longitude error lambda modulated by double-axis rotation3The difference value of (a) to (b),x1、y1、z1respectively the gyro constant drift of the corresponding coordinate axis under the coordinate system of the single-axis rotation modulation laser gyro navigation inertial navigation 1 body,x2、y2、z2respectively the gyro constant drift of the corresponding coordinate axis under the biaxial rotation modulation laser gyro navigation inertial navigation 2 body coordinate system,x3、y3、z3the gyro constant drift of corresponding coordinate axes under a biaxial rotation modulation laser gyro navigation inertial navigation 3 body coordinate system is ▽x1、▽y1The accelerometer constant values of the corresponding horizontal coordinate axes of the single-axis rotation modulation laser gyro navigation inertial navigation 1 are zero offset respectively, ▽x2、▽y2The accelerometer constant values of the two-axis rotation modulation laser gyro navigation inertial navigation system 2 corresponding horizontal coordinate axes are zero offset respectively, ▽x3、▽y3Respectively, the accelerometer constant values of the corresponding horizontal coordinate axes of the biaxial rotation modulation laser gyro navigation inertial navigation 3 are zero offset, and the superscript T represents transposition;
step two: respectively establishing joint error state equations between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 2, and between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 3, wherein the joint error state equations are respectively
Wherein, the system state matrix is respectively:
vE、vNeast-direction speed, north-direction speed, omega of naval vesselieIs the rotational angular velocity of the earth, L is the latitude position of the naval vessel, h is the height of the naval vessel, RE、RNRespectively, the curvature radius of the Mao-unitary ring and the meridian radius fE、fN、fUAre respectively east, north and sky specific force values,respectively are attitude matrixes of a single-axis rotation modulation laser gyro navigation inertial navigation system 1 and double-axis rotation modulation laser gyro navigation inertial navigation systems 2 and 3,respectively is a submatrix formed by the first two rows and the first two columns of the attitude matrixes of a single-axis rotation modulation laser gyro navigation inertial navigation 1 and double-axis rotation modulation laser gyro navigation inertial navigation 2 and 3 respectively, and 0i×jA zero matrix representing i rows and j columns;
the system noise driving matrix is respectively:
the system noise is:
respectively modulating the gyro noise of corresponding coordinate axes under a body coordinate system of the laser gyro navigation inertial navigation system 1 by single-axis rotation,respectively modulating the gyro noise of corresponding coordinate axes under a 2-body coordinate system of the laser gyro navigation inertial navigation system by biaxial rotation,respectively modulating the gyro noise of corresponding coordinate axes under a navigation inertial navigation system 3 body coordinate system of the laser gyro by biaxial rotation,respectively are accelerometer noises of corresponding horizontal coordinate axes under a uniaxial rotation modulation laser gyro navigation inertial navigation 1 body coordinate system,respectively modulating the accelerometer noise of corresponding horizontal coordinate axes under a navigation inertial navigation system 2 body coordinate system of the laser gyro by biaxial rotation,respectively modulating the accelerometer noise of the corresponding horizontal coordinate axis under a navigation inertial navigation system 3 body coordinate system of the laser gyroscope in a biaxial rotation manner;
step three: respectively establishing observation equations between a single-axis rotation modulation laser gyro navigation inertial navigation system 1 and a double-axis rotation modulation laser gyro navigation inertial navigation system 2, between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and a double-axis rotation modulation laser gyro navigation inertial navigation system 3, wherein the observed quantities are the speed difference and the position difference between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 2 and 3 after the lever arm effect is deducted, and the observation equations are respectively the speed difference and the position difference between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation
z12(t)＝Hx12(t)+v(t),z13(t)＝Hx13(t)+v(t) (12)
Wherein,
z12(t)＝[vE12vN12L12λ12]T,z13(t)＝[vE13vN13L13λ13]T(13)
v (t) is the observation matrix, and v (t) is the observation noise;
z12(t)、z13(t) respectively showing the observed quantity between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation systems 2 and 3,indicating single axis rotation modulated laser gyro navigationEast output velocity of inertial navigation system 1East direction output speed of laser gyro navigation inertial navigation system 2 is modulated with double-shaft rotationThe difference value of (a) to (b),representing the north output speed of the single-axis rotation modulation laser gyro navigation inertial navigation system 1And the double-shaft rotation modulation laser gyro navigation inertial navigation 2 northbound output speedThe difference value of (a) to (b),shows the east output speed of the single-axis rotation modulation laser gyro navigation inertial navigation system 1East output speed of laser gyro navigation inertial navigation 3 is modulated with double-shaft rotationThe difference value of (a) to (b),representing the north output speed of the single-axis rotation modulation laser gyro navigation inertial navigation system 1And the double-shaft rotation modulation laser gyro navigation inertial navigation 3 northbound output speedThe difference value of (a) to (b),representing the output latitude of the single-axis rotation modulation laser gyro navigation inertial navigation system 1Output latitude of laser gyro navigation inertial navigation 2 modulated by double-shaft rotationThe difference value of (a) to (b),representing the output longitude of a single-axis rotation modulation laser gyro navigation inertial navigation system 1Output longitude of laser gyro navigation inertial navigation system 2 modulated by double-shaft rotationThe difference value of (a) to (b),representing the output latitude of the single-axis rotation modulation laser gyro navigation inertial navigation system 1And the output latitude of the biaxial rotation modulation laser gyro navigation inertial navigation 3The difference value of (a) to (b),representing the output longitude of a single-axis rotation modulation laser gyro navigation inertial navigation system 1Output longitude of laser gyro navigation inertial navigation system 3 modulated by double-shaft rotationDifference of (A) to (B), I2×2Representing a second order identity matrix;
step four: determining the influence of system noise on the drift estimation value of the single-axis rotation modulation laser gyroscope navigation inertial navigation azimuth gyroscope, and realizing the following steps:
1) determining a steady state estimation error covariance matrix for the system state corresponding to the joint error state Kalman filter
Deducting the influence of lever arm errors caused by installation relation, the theoretical value of the speed difference and the position difference between the single-axis rotation modulation laser gyro navigation inertial navigation 1 and the double-axis rotation modulation laser gyro navigation inertial navigation 2 and 3 is 0, which can be approximated to be free of observation noise, and the steady state estimation error covariance matrix P of the corresponding system state of the joint error state Kalman filter meets the requirement of no observation noise
P＝(I-KH)FPFT(I-KH)T+(I-KH)GQGT(I-KH)T(14)
K is Kalman filtering gain, Q is a set value of a Kalman filter system noise covariance matrix, F is a system state matrix, H is an observation matrix, G is a system noise matrix, and I is an identity matrix;
2) determining a true system noise covariance matrixThe relation between the set value of the noise covariance matrix of the Kalman filter system is
Wherein alpha is an unknown scalar and represents the difference between the real noise covariance matrix and a set value; if alpha is more than 0, the real system noise covariance matrix is larger than the set value; if alpha is less than 0, the real system noise covariance matrix is smaller than the set value; if alpha is 0, the real system noise covariance matrix is equal to the set value;
3) determining a steady state estimation error covariance matrix for the system state corresponding to the true system noise covariance matrixIs composed of
4) Determining a change Δ P in the state estimation error covariance caused by an inconsistency between the true noise covariance matrix and the Kalman filter system noise covariance matrix set point as
5) Determining the influence of system noise on the drift estimation value of the single-axis rotation modulation laser gyro navigation inertial navigation azimuth gyro
According to the formula (16) in the step 4), if the real system noise covariance matrix is larger than the set value, that is, α is larger than 0, the variance of the real system state estimation error is larger than the variance of the nominal system state estimation error; if the real system noise covariance matrix is smaller than the nominal value, namely alpha is less than 0, the variance of the real system state estimation error is less than the variance of the nominal system state estimation error; for a steady-state Kalman filter, the smaller the variance of system state estimation errors is, the smaller the standard deviation of corresponding system state estimation values is, and the smaller the standard deviation of corresponding single-axis rotation modulation laser gyro navigation inertial navigation 1 azimuth gyro drift estimation values is;
step five: performing Kalman filtering according to a system state equation and an observation equation between a single-axis rotation modulation laser gyro navigation inertial navigation device 1 and double-axis rotation modulation laser gyro navigation inertial navigation devices 2 and 3 respectively, estimating respective system states, finishing online estimation of relative performance between the double-axis rotation modulation laser gyro navigation inertial navigation devices 2 and 3 by taking a standard difference of azimuth gyro drift estimation values of the single-axis rotation modulation laser gyro navigation inertial navigation device 1 after two Kalman filters are stabilized as an evaluation index, wherein random errors of the double-axis rotation modulation laser gyro navigation inertial navigation devices corresponding to the filters with smaller standard differences of the azimuth gyro drift estimation values of the single-axis rotation modulation laser gyro navigation inertial navigation device 1 in the same time period are smaller, and the positioning precision is higher;
azimuth gyro drift estimation value standard deviation sigma of single-axis rotation modulation laser gyro navigation inertial navigation 1 obtained by Kalman filter estimation composed of single-axis rotation modulation laser gyro navigation inertial navigation 1 and double-axis rotation modulation laser gyro navigation inertial navigation 22(z1) The standard deviation sigma of the azimuth gyro drift estimation value of the single-axis rotation modulation laser gyro navigation inertial navigation 1 is obtained by the Kalman filter estimation composed of the single-axis rotation modulation laser gyro navigation inertial navigation 1 and the double-axis rotation modulation laser gyro navigation inertial navigation 33(z1) Respectively as follows:
calculating the standard deviation of the single-axis rotation modulation laser gyro navigation inertial navigation 1 azimuth gyro drift estimation value once every fixed time length, and comparing the random error of the two filters corresponding to the double-axis rotation modulation laser gyro navigation inertial navigation by taking the standard deviation as an index; wherein N is the number of the azimuth gyro drift estimated values of the uniaxial rotation modulation laser gyro navigation inertial navigation 1 in the time period,the mean value of the azimuth gyro drift estimated values of the single-axis rotation modulation laser gyro navigation inertial navigation 1 in the time period is obtained;
if σ2(z1)＜σ3(z1) If so, the random error of the biaxial rotation modulation laser gyro navigation inertial navigation system 2 is smaller, the positioning precision is higher, and the biaxial rotation modulation laser gyro navigation inertial navigation system 2 is selected as a main inertial navigation system;
if σ2(z1)＞σ3(z1) If so, the random error of the biaxial rotation modulation laser gyro navigation inertial navigation system 3 is smaller, the positioning precision is higher, and the biaxial rotation modulation laser gyro navigation inertial navigation system 3 is selected as a main inertial navigation system;
step six: using the uniaxial rotation modulation laser gyroscope navigation inertial navigation 1 azimuth gyroscope drift with smaller standard deviation estimated in the fifth step as a final estimation value, and performing prediction compensation on the deterministic long-term positioning error caused by the final estimation value, wherein the compensation mode is output correction;
the prediction compensation step of the deterministic long-term positioning error caused by the drift of the azimuth gyroscope of the single-axis rotation modulation laser gyroscope navigation inertial navigation 1 comprises the following steps:
1) determining the error state x of the single-axis rotation modulation laser gyro navigation inertial navigation system 11(t) is
x1(t)＝[φE1φN1φU1vE1vN1L1λ1]T(18)
Wherein phi isE1For the single-axis rotation modulation of the east attitude error, phi, of the laser gyro navigation inertial navigation system 1N1For single-axis rotation modulation of the north attitude error, phi, of the laser gyro navigation inertial navigation system 1U1For single-axis rotation modulation of the attitude error, v, of the laser gyro navigation inertial navigation system 1E1For the uniaxial rotation modulation of the east velocity error, v, of the laser gyro navigation inertial navigation 1N1For the single-axis rotation modulation of the north velocity error, L, of the laser gyro navigation inertial navigation system 11For single-axis rotation modulation of latitude error, lambda, of laser gyro navigation inertial navigation 11The longitude error of the laser gyro navigation inertial navigation system 1 is modulated by single-axis rotation;
2) determining the external input quantity u formed by gyro drift and accelerometer zero offset in the error state equation of the single-axis rotation modulation laser gyro navigation inertial navigation 11(t) is u1(t)＝[x1 y1 z1▽x1▽y1]T；
3) Constructing an error state equation of the single-axis rotation modulation laser gyro navigation inertial navigation 1
Wherein,
A1(t) is the system state matrix, B1(t) is an external input matrix, G1(t) is a system noise matrix;
the method comprises the following steps of modulating system noise consisting of gyro noise and accelerometer noise of the laser gyro navigation inertial navigation system 1 for single-axis rotation;
4) obtaining an error state prediction equation of a discretized single-axis rotation modulation laser gyro navigation inertial navigation system 1 from an error state equation (19)
Wherein,is the system state x1Discrete amount of (t), phi1(k) Is a system state matrix A1(t) a discrete matrix of the plurality of discrete matrices,1(k) for external input matrix B1(t) a discrete matrix of the plurality of discrete matrices,for external input u1(t), k +1 are discretization time, initial time
5) And carrying out prediction compensation on the deterministic long-term positioning error caused by the drift of the azimuth gyroscope of the single-axis rotation modulation laser gyroscope navigation inertial navigation 1 according to an error state prediction equation by Kalman filtering, wherein the compensation mode is output correction.
The laser gyro navigation inertial navigation redundancy configuration is realized through the steps as follows: a. and (b) preferably selecting an inertial navigation system with better performance (smaller random error) from the two sets of biaxial rotation modulation laser gyro navigation inertial navigation systems as a main inertial navigation system, and ensuring that an optimal navigation positioning result is obtained b. Through information fusion among inertial navigation systems, the cooperative positioning among the navigation inertial navigation systems with the laser gyro in redundant configuration is realized. The method is also suitable for the problem of cooperative positioning under the condition of single-axis rotation modulation laser gyro navigation inertial navigation and redundancy configuration of more than two sets of double-axis rotation modulation laser gyro navigation inertial navigation.
Compared with the prior art, the invention has the beneficial effects that:
1) the online evaluation of the relative performance between two sets of double-axis rotation modulation laser gyro navigation inertial navigations which are redundantly configured under the condition of no external reference information is realized, the double-axis rotation modulation laser gyro navigation inertial navigations with smaller random errors are preferably selected as the main inertial navigation, and the optimal navigation positioning result is ensured to be obtained;
2) the positioning accuracy of the single-axis rotation modulation laser gyro navigation inertial navigation is improved, even if two sets of double-axis rotation modulation laser gyro navigation inertial navigation simultaneously fail to generate extreme conditions under the condition of long navigation, the single-axis rotation modulation laser gyro navigation inertial navigation which compensates over-determinacy positioning errors can provide high-accuracy positioning, and the method has great significance for improving the viability of the naval vessel under severe sea conditions;
3) the method for redundantly configuring the laser gyro navigation inertial navigation co-location solves the problem of information fusion between inertial navigation systems under the condition of no external reference information, and maximizes the information utilization.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a comparison graph of standard deviation curves of the single-axis rotation modulation laser gyro navigation inertial navigation azimuth gyro drift estimation values;
FIG. 3 is a comparison diagram of position errors of two sets of biaxial rotation modulation laser gyro navigation inertial navigations;
FIG. 4 is a comparison diagram of position errors of laser gyro navigation inertial navigation modulated by single-axis rotation before and after co-location.
Detailed Description
The method of the present invention is further described in detail below with reference to the accompanying drawings.
Fig. 1 is a schematic flow diagram of the present invention, and a method for redundantly configuring a laser gyro navigation inertial navigation cooperative positioning includes the following steps:
the method comprises the following steps: respectively determining the joint error states between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 2, the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 3, wherein the joint error states are respectively
x12(t)＝[φE12φN12φU12vE12vN12L12λ12 x1 y1 z1 x2 y2 z2▽x1▽y1▽x2▽y2]T(22)
x13(t)＝[φE13φN13φU13vE13vN13L13λ13 x1 y1 z1 x3 y3 z3▽x1▽y1▽x3▽y3]T(23)
Wherein x is12(t) is the combined error state between the single-axis rotation modulation laser gyro navigation inertial navigation 1 and the double-axis rotation modulation laser gyro navigation inertial navigation 2, x13(t) is the combined error state phi between the single-axis rotation modulation laser gyro navigation inertial navigation 1 and the double-axis rotation modulation laser gyro navigation inertial navigation 3E12＝φE1-φE2Modulating laser gyro navigation inertial navigation 1 east attitude error phi for single axis rotationE1Laser gyro navigation inertial navigation 2 east attitude error phi modulated by double-axis rotationE2Difference of (phi)N12＝φN1-φN2Modulating laser gyro navigation inertial navigation 1 north attitude error phi for single axis rotationN1And biaxial rotation modulation laser gyro navigation inertial navigation 2 north attitude error phiN2Difference of (phi)U12＝φU1-φU21-day attitude error phi of laser gyro navigation inertial navigation modulated by single-axis rotationU1And the biaxial rotation modulation laser gyro navigation inertial navigation 2-day attitude error phiU2Difference of (phi)E13＝φE1-φE3Modulating laser gyro navigation inertial navigation 1 east attitude error phi for single axis rotationE1Laser gyro navigation inertial navigation 3 east attitude error phi modulated by double-axis rotationE3Difference of (phi)N13＝φN1-φN3Modulating laser gyro navigation inertial navigation 1 north attitude error phi for single axis rotationN1And the double-shaft rotation modulation laser gyro navigation inertial navigation 3 north attitude error phiN3Difference of (phi)U13＝φU1-φU31-day attitude error phi of laser gyro navigation inertial navigation modulated by single-axis rotationU13-day attitude error phi of laser gyro navigation inertial navigation modulated by double-axis rotationU3Difference of vE12＝vE1-vE2Modulating laser gyro navigation inertial navigation 1 east direction velocity error v for single axis rotationE1And biaxial rotation modulation laser gyro navigation inertial navigation 2 east direction velocity error vE2Difference of vN12＝vN1-vN2Modulating laser gyro navigation inertial navigation 1 north velocity error v for single axis rotationN1And biaxial rotation modulation laser gyro navigation inertial navigation 2 north direction velocity error vN2Difference of vE13＝vE1-vE3Modulating laser gyro navigation inertial navigation 1 east direction velocity error v for single axis rotationE1And biaxial rotation modulation laser gyro navigation inertial navigation 3 east direction velocity error vE3Difference of vN13＝vN1-vN3Modulating laser gyro navigation inertial navigation 1 north velocity error v for single axis rotationN1And biaxial rotation modulation laser gyro navigation inertial navigation 3 north direction velocity error vN3Difference of (D), L12＝L1-L2Method for modulating 1 latitude error L of laser gyro navigation inertial navigation for single-axis rotation12-latitude error L of navigation inertial navigation of laser gyro modulated by double-axis rotation2A difference of (a)12＝λ1-λ2Method for modulating 1 longitude error lambda of laser gyro navigation inertial navigation for single-axis rotation1Laser gyro navigation inertial navigation 2 longitude error lambda modulated by double-axis rotation2Difference of (D), L13＝L1-L3Method for modulating 1 latitude error L of laser gyro navigation inertial navigation for single-axis rotation1Laser gyro navigation inertial navigation 3 latitude error L modulated by double-shaft rotation3A difference of (a)13＝λ1-λ3Method for modulating 1 longitude error lambda of laser gyro navigation inertial navigation for single-axis rotation1Laser gyro navigation inertial navigation 3 longitude error lambda modulated by double-axis rotation3The difference value of (a) to (b),x1、y1、z1respectively the gyro constant drift of the corresponding coordinate axis under the coordinate system of the single-axis rotation modulation laser gyro navigation inertial navigation 1 body,x2、y2、z2gyroscope respectively modulating corresponding coordinate axes of laser gyroscope navigation inertial navigation 2 body coordinate system by double-shaft rotationThe drift of the constant value is caused by the drift of the constant value,x3、y3、z3the gyro constant drift of corresponding coordinate axes under a biaxial rotation modulation laser gyro navigation inertial navigation 3 body coordinate system is ▽x1、▽y1The accelerometer constant values of the corresponding horizontal coordinate axes of the single-axis rotation modulation laser gyro navigation inertial navigation 1 are zero offset respectively, ▽x2、▽y2The accelerometer constant values of the two-axis rotation modulation laser gyro navigation inertial navigation system 2 corresponding horizontal coordinate axes are zero offset respectively, ▽x3、▽y3Respectively, the accelerometer constant values of the corresponding horizontal coordinate axes of the biaxial rotation modulation laser gyro navigation inertial navigation 3 are zero offset, and the superscript T represents transposition;
step two: respectively establishing joint error state equations between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 2, and between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 3, wherein the joint error state equations are respectively
Wherein, the system state matrix is respectively:
vE、vNeast-direction speed, north-direction speed, omega of naval vesselieIs the rotational angular velocity of the earth, L is the latitude position of the naval vessel, h is the height of the naval vessel, RE、RNRespectively, the curvature radius of the Mao-unitary ring and the meridian radius fE、fN、fUAre respectively east, north and sky specific force values,respectively are attitude matrixes of a single-axis rotation modulation laser gyro navigation inertial navigation system 1 and double-axis rotation modulation laser gyro navigation inertial navigation systems 2 and 3,respectively is a submatrix formed by the first two rows and the first two columns of the attitude matrixes of a single-axis rotation modulation laser gyro navigation inertial navigation 1 and double-axis rotation modulation laser gyro navigation inertial navigation 2 and 3 respectively, and 0i×jA zero matrix representing i rows and j columns;
the system noise driving matrix is respectively:
the system noise is:
respectively modulating the gyro noise of corresponding coordinate axes under a body coordinate system of the laser gyro navigation inertial navigation system 1 by single-axis rotation,respectively modulating the gyro noise of corresponding coordinate axes under a 2-body coordinate system of the laser gyro navigation inertial navigation system by biaxial rotation,respectively modulating the gyro noise of corresponding coordinate axes under a navigation inertial navigation system 3 body coordinate system of the laser gyro by biaxial rotation,respectively are accelerometer noises of corresponding horizontal coordinate axes under a uniaxial rotation modulation laser gyro navigation inertial navigation 1 body coordinate system,respectively modulating the accelerometer noise of corresponding horizontal coordinate axes under a navigation inertial navigation system 2 body coordinate system of the laser gyro by biaxial rotation,respectively modulating the accelerometer noise of the corresponding horizontal coordinate axis under a navigation inertial navigation system 3 body coordinate system of the laser gyroscope in a biaxial rotation manner;
step three: respectively establishing observation equations between a single-axis rotation modulation laser gyro navigation inertial navigation system 1 and a double-axis rotation modulation laser gyro navigation inertial navigation system 2, between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 3, wherein the observed quantities are the speed difference and the position difference between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 2 and 3 after the lever arm effect is deducted, the observation update period of the embodiment is 1s, and the observation equations are respectively the difference of the speed and the position
z12(t)＝Hx12(t)+v(t),z13(t)＝Hx13(t)+v(t) (33)
Wherein,
z12(t)＝[vE12vN12L12λ12]T,z13(t)＝[vE13vN13L13λ13]T(34)
v (t) is the observation matrix, and v (t) is the observation noise;
z12(t)、z13(t) respectively showing the observed quantity between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation systems 2 and 3,shows the east output speed of the single-axis rotation modulation laser gyro navigation inertial navigation system 1East direction output speed of laser gyro navigation inertial navigation system 2 is modulated with double-shaft rotationThe difference value of (a) to (b),representing the north output speed of the single-axis rotation modulation laser gyro navigation inertial navigation system 1And the double-shaft rotation modulation laser gyro navigation inertial navigation 2 northbound output speedThe difference value of (a) to (b),shows the east output speed of the single-axis rotation modulation laser gyro navigation inertial navigation system 1East output speed of laser gyro navigation inertial navigation 3 is modulated with double-shaft rotationThe difference value of (a) to (b),representing the north output speed of the single-axis rotation modulation laser gyro navigation inertial navigation system 1And the double-shaft rotation modulation laser gyro navigation inertial navigation 3 northbound output speedThe difference value of (a) to (b),representing the output latitude of the single-axis rotation modulation laser gyro navigation inertial navigation system 1Output latitude of laser gyro navigation inertial navigation 2 modulated by double-shaft rotationThe difference value of (a) to (b),representing the output longitude of a single-axis rotation modulation laser gyro navigation inertial navigation system 1Output longitude of laser gyro navigation inertial navigation system 2 modulated by double-shaft rotationThe difference value of (a) to (b),indicating a single axis of rotationOutput latitude of rotary modulation laser gyro navigation inertial navigation 1And the output latitude of the biaxial rotation modulation laser gyro navigation inertial navigation 3The difference value of (a) to (b),representing the output longitude of a single-axis rotation modulation laser gyro navigation inertial navigation system 1Output longitude of laser gyro navigation inertial navigation system 3 modulated by double-shaft rotationDifference of (A) to (B), I2×2Representing a second order identity matrix;
step four: determining the influence of system noise on the drift estimation value of the single-axis rotation modulation laser gyroscope navigation inertial navigation azimuth gyroscope, and realizing the following steps:
1) determining a steady state estimation error covariance matrix for the system state corresponding to the joint error state Kalman filter
Deducting the influence of lever arm errors caused by installation relation, the theoretical value of the speed difference and the position difference between the single-axis rotation modulation laser gyro navigation inertial navigation 1 and the double-axis rotation modulation laser gyro navigation inertial navigation 2 and 3 is 0, which can be approximated to be free of observation noise, and the steady state estimation error covariance matrix P of the corresponding system state of the joint error state Kalman filter meets the requirement of no observation noise
P＝(I-KH)FPFT(I-KH)T+(I-KH)GQGT(I-KH)T(35)
K is Kalman filtering gain, Q is a set value of a Kalman filter system noise covariance matrix, F is a system state matrix, H is an observation matrix, G is a system noise matrix, and I is an identity matrix;
2) determining a true system noise covariance matrixThe relation between the set value of the noise covariance matrix of the Kalman filter system is
Wherein alpha is an unknown scalar and represents the difference between the real noise covariance matrix and a set value; if alpha is more than 0, the real system noise covariance matrix is larger than the set value; if alpha is less than 0, the real system noise covariance matrix is smaller than the set value; if alpha is 0, the real system noise covariance matrix is equal to the set value;
3) determining a steady state estimation error covariance matrix for the system state corresponding to the true system noise covariance matrixIs composed of
4) Determining a change Δ P in the state estimation error covariance caused by an inconsistency between the true noise covariance matrix and the Kalman filter system noise covariance matrix set point as
5) Determining the influence of system noise on the drift estimation value of the single-axis rotation modulation laser gyro navigation inertial navigation azimuth gyro
According to the formula (37) in the step 4), if the real system noise covariance matrix is larger than the set value, that is, α is larger than 0, the variance of the real system state estimation error is larger than the variance of the nominal system state estimation error; if the real system noise covariance matrix is smaller than the nominal value, namely alpha is less than 0, the variance of the real system state estimation error is less than the variance of the nominal system state estimation error; for a steady-state Kalman filter, the smaller the variance of system state estimation errors is, the smaller the standard deviation of corresponding system state estimation values is, and the smaller the standard deviation of corresponding single-axis rotation modulation laser gyro navigation inertial navigation 1 azimuth gyro drift estimation values is;
step five: performing Kalman filtering according to a system state equation and an observation equation between a single-axis rotation modulation laser gyro navigation inertial navigation device 1 and double-axis rotation modulation laser gyro navigation inertial navigation devices 2 and 3 respectively, estimating respective system states, finishing online estimation of relative performance between the double-axis rotation modulation laser gyro navigation inertial navigation devices 2 and 3 by taking a standard difference of azimuth gyro drift estimation values of the single-axis rotation modulation laser gyro navigation inertial navigation device 1 after two Kalman filters are stabilized as an evaluation index, wherein random errors of the double-axis rotation modulation laser gyro navigation inertial navigation devices corresponding to the filters with smaller standard differences of the azimuth gyro drift estimation values of the single-axis rotation modulation laser gyro navigation inertial navigation device 1 in the same time period are smaller, and the positioning precision is higher;
azimuth gyro drift estimation value standard deviation sigma of single-axis rotation modulation laser gyro navigation inertial navigation 1 obtained by Kalman filter estimation composed of single-axis rotation modulation laser gyro navigation inertial navigation 1 and double-axis rotation modulation laser gyro navigation inertial navigation 22(z1) The standard deviation sigma of the azimuth gyro drift estimation value of the single-axis rotation modulation laser gyro navigation inertial navigation 1 is obtained by the Kalman filter estimation composed of the single-axis rotation modulation laser gyro navigation inertial navigation 1 and the double-axis rotation modulation laser gyro navigation inertial navigation 33(z1) Respectively as follows:
calculating the standard deviation of the single-axis rotation modulation laser gyroscope navigation inertial navigation 1 azimuth gyroscope drift estimation value every 4h, and comparing the random error of the two filters corresponding to the double-axis rotation modulation laser gyroscope navigation inertial navigation by taking the standard deviation as an index; wherein N is the number of the azimuth gyro drift estimated values of the uniaxial rotation modulation laser gyro navigation inertial navigation 1 in the time period,the mean value of the azimuth gyro drift estimated values of the single-axis rotation modulation laser gyro navigation inertial navigation 1 in the time period is obtained;
if σ2(z1)＜σ3(z1) If so, the random error of the biaxial rotation modulation laser gyro navigation inertial navigation system 2 is smaller, the positioning precision is higher, and the biaxial rotation modulation laser gyro navigation inertial navigation system 2 is selected as a main inertial navigation system;
if σ2(z1)＞σ3(z1) If so, the random error of the biaxial rotation modulation laser gyro navigation inertial navigation system 3 is smaller, the positioning precision is higher, and the biaxial rotation modulation laser gyro navigation inertial navigation system 3 is selected as a main inertial navigation system;
step six: using the uniaxial rotation modulation laser gyroscope navigation inertial navigation 1 azimuth gyroscope drift with smaller standard deviation estimated in the fifth step as a final estimation value, and performing prediction compensation on the deterministic long-term positioning error caused by the final estimation value, wherein the compensation mode is output correction;
the prediction compensation step of the deterministic long-term positioning error caused by the drift of the azimuth gyroscope of the single-axis rotation modulation laser gyroscope navigation inertial navigation 1 comprises the following steps:
1) determining the error state x of the single-axis rotation modulation laser gyro navigation inertial navigation system 11(t) is
x1(t)＝[φE1φN1φU1vE1vN1L1λ1]T(39)
Wherein phi isE1For the single-axis rotation modulation of the east attitude error, phi, of the laser gyro navigation inertial navigation system 1N1For single-axis rotation modulation of the north attitude error, phi, of the laser gyro navigation inertial navigation system 1U1For single-axis rotation modulation of the attitude error, v, of the laser gyro navigation inertial navigation system 1E1For the uniaxial rotation modulation of the east velocity error, v, of the laser gyro navigation inertial navigation 1N1For the single-axis rotation modulation of the north velocity error, L, of the laser gyro navigation inertial navigation system 11For single-axis rotation modulation of latitude error, lambda, of laser gyro navigation inertial navigation 11The longitude error of the laser gyro navigation inertial navigation system 1 is modulated by single-axis rotation;
2) determining the external input quantity u formed by gyro drift and accelerometer zero offset in the error state equation of the single-axis rotation modulation laser gyro navigation inertial navigation 11(t) is u1(t)＝[x1 y1 z1▽x1▽y1]T；
3) Constructing an error state equation of the single-axis rotation modulation laser gyro navigation inertial navigation 1
Wherein,
A1(t) is the system state matrix, B1(t) is an external input matrix, G1(t) is a system noise matrix;
the method comprises the following steps of modulating system noise consisting of gyro noise and accelerometer noise of the laser gyro navigation inertial navigation system 1 for single-axis rotation;
4) obtaining an error state prediction equation of a discretized single-axis rotation modulation laser gyro navigation inertial navigation system 1 from an error state equation (40)
Wherein,is the system state x1Discrete amount of (t), phi1(k) Is a system state matrix A1(t) a discrete matrix of the plurality of discrete matrices,1(k) for external input matrix B1(t) a discrete matrix of the plurality of discrete matrices,for external input u1(t), k +1 are discretization time, initial time
5) And carrying out prediction compensation on the deterministic long-term positioning error caused by the drift of the azimuth gyroscope of the single-axis rotation modulation laser gyroscope navigation inertial navigation 1 according to an error state prediction equation by Kalman filtering, wherein the compensation mode is output correction.
And performing a semi-physical simulation experiment according to the steps to verify the effect of the method.
The single-shaft rotation modulation laser gyro navigation inertial navigation system 1 performs four-position rotation and stop modulation around an azimuth axis, and the stop angle relative to the zero position of a rotating mechanism is 0 degree, 90 degrees, 180 degrees and 270 degrees; the biaxial rotation modulation laser gyro navigation inertial navigation systems 2 and 3 rotate and stop around the azimuth axis and the roll axis in 16 orders, and the stop angle of the zero positions of the two directions relative to the rotating mechanism is 0 degree and 180 degrees.
The noise data of the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation systems 2 and 3 are obtained by subtracting the average value from three sets of different high-precision laser gyro navigation inertial navigation long-term (120h) static test data, and the noise condition of the system can be truly reflected.
The error parameters of the single-axis rotation modulation laser gyro navigation inertial navigation device 1 are set as a) the horizontal gyro drift is respectively 0.003 degree/h and-0.002 degree/h, the azimuth gyro drift is 0.0005 degree/h (the laser gyro drift set value is based on the requirement on the laser gyro precision in the single-axis rotation modulation laser gyro navigation inertial navigation error distribution scheme with the positioning precision superior to 1nm/72 h), and b) the accelerometer constant zero offset is respectively 2 × 10-5g、-4×10-5g (days not considered).
The error parameters of the biaxial rotation modulation laser gyro navigation inertial navigation systems 2 and 3 are set as a) the gyro constant drift is respectively 0.004 degree/h, -0.005 degree/h and 0.003 degree/h, and b) the accelerometer constant zero offset is respectively 2 × 10-5g、-3×10-5g (days not considered).
And (3) respectively calculating the standard deviation of the azimuth gyro drift estimation value of the single-axis rotation modulation laser gyro navigation inertial navigation 1 in the combined error state Kalman filter consisting of the double-axis rotation modulation laser gyro navigation inertial navigation 2 and 3 and the single-axis rotation modulation laser gyro navigation inertial navigation 1 according to a formula (38) in the fifth step, and calculating from the 16 th hour after the filter is stabilized, and calculating once every 4 hours. FIG. 2 shows a standard deviation curve of the azimuth gyro drift estimation value of the uniaxial rotation modulation laser gyro navigation inertial navigation 1 of the two filters in the fifth step, and the whole shows sigma3(z1)＞σ2(z1) The random error of the biaxial rotation modulation laser gyro navigation inertial navigation system 2 can be judged to be relatively small according to the trend.
Fig. 3 shows a position error curve of the biaxial rotation modulation laser gyro navigation inertial navigations 2 and 3, wherein the random error of the biaxial rotation modulation laser gyro navigation inertial navigation 2 is wholly smaller than that of the biaxial rotation modulation laser gyro navigation inertial navigation 3, and is consistent with the online evaluation result of the relative performance between the biaxial rotation modulation laser gyro navigation inertial navigations.
And (3) predicting and compensating the deterministic long-term positioning error caused by the biaxial rotation modulation laser gyro navigation inertial navigation 2 and the uniaxial rotation modulation laser gyro navigation inertial navigation 1 according to the sixth step by taking the standard deviation of the azimuth gyro drift estimation value of the uniaxial rotation modulation laser gyro navigation inertial navigation 1 obtained by the joint error state Kalman filter estimation as the final estimation value. Fig. 4 shows a position error curve before and after compensation, and it can be seen that the positioning accuracy of the single-axis rotation modulation laser gyro navigation inertial navigation system is greatly improved by the cooperative positioning method in the invention, and the viability of the naval vessel in a severe sea condition environment is improved under the condition of ensuring the reliability of naval vessel navigation positioning.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned examples, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that various modifications and adaptations to those skilled in the art without departing from the principles of the present invention should be considered as within the scope of the present invention.

Claims (1)

1. The method for redundantly configuring the laser gyro navigation inertial navigation cooperative positioning is characterized by comprising the following steps of:
the method comprises the following steps: respectively determining the joint error states between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 2, the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 3, wherein the joint error states are respectively
<mrow> <msub> <mi>x</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;phi;</mi> <mrow> <mi>E</mi> <mn>12</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;phi;</mi> <mrow> <mi>N</mi> <mn>12</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;phi;</mi> <mrow> <mi>U</mi> <mn>12</mn> </mrow> </msub> </mtd> <mtd> <mrow> <msub> <mi>&amp;delta;v</mi> <mrow> <mi>E</mi> <mn>12</mn> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;delta;v</mi> <mrow> <mi>N</mi> <mn>12</mn> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;delta;L</mi> <mn>12</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;delta;&amp;lambda;</mi> <mn>12</mn> </msub> </mrow> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>y</mi> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>y</mi> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>y</mi> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>x</mi> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>y</mi> <mn>2</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>x</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;phi;</mi> <mrow> <mi>E</mi> <mn>13</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;phi;</mi> <mrow> <mi>N</mi> <mn>13</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;phi;</mi> <mrow> <mi>U</mi> <mn>13</mn> </mrow> </msub> </mtd> <mtd> <mrow> <msub> <mi>&amp;delta;v</mi> <mrow> <mi>E</mi> <mn>13</mn> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;delta;v</mi> <mrow> <mi>N</mi> <mn>13</mn> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;delta;L</mi> <mn>13</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;delta;&amp;lambda;</mi> <mn>13</mn> </msub> </mrow> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>y</mi> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>y</mi> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>y</mi> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>x</mi> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>y</mi> <mn>3</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
Wherein,x12(t) is the combined error state between the single-axis rotation modulation laser gyro navigation inertial navigation 1 and the double-axis rotation modulation laser gyro navigation inertial navigation 2, x13(t) is the combined error state phi between the single-axis rotation modulation laser gyro navigation inertial navigation 1 and the double-axis rotation modulation laser gyro navigation inertial navigation 3E12＝φE1-φE2Modulating laser gyro navigation inertial navigation 1 east attitude error phi for single axis rotationE1Laser gyro navigation inertial navigation 2 east attitude error phi modulated by double-axis rotationE2Difference of (phi)N12＝φN1-φN2Modulating laser gyro navigation inertial navigation 1 north attitude error phi for single axis rotationN1And biaxial rotation modulation laser gyro navigation inertial navigation 2 north attitude error phiN2Difference of (phi)U12＝φU1-φU21-day attitude error phi of laser gyro navigation inertial navigation modulated by single-axis rotationU1And the biaxial rotation modulation laser gyro navigation inertial navigation 2-day attitude error phiU2Difference of (phi)E13＝φE1-φE3Modulating laser gyro navigation inertial navigation 1 east attitude error phi for single axis rotationE1Laser gyro navigation inertial navigation 3 east attitude error phi modulated by double-axis rotationE3Difference of (phi)N13＝φN1-φN3Modulating laser gyro navigation inertial navigation 1 north attitude error phi for single axis rotationN1And the double-shaft rotation modulation laser gyro navigation inertial navigation 3 north attitude error phiN3Difference of (phi)U13＝φU1-φU31-day attitude error phi of laser gyro navigation inertial navigation modulated by single-axis rotationU13-day attitude error phi of laser gyro navigation inertial navigation modulated by double-axis rotationU3Difference of vE12＝vE1-vE2Modulating laser gyro navigation inertial navigation 1 east direction velocity error v for single axis rotationE1And biaxial rotation modulation laser gyro navigation inertial navigation 2 east direction velocity error vE2Difference of vN12＝vN1-vN2Modulating laser gyro navigation inertial navigation 1 north velocity error v for single axis rotationN1And biaxial rotation modulation laser gyro navigation inertial navigation 2 north direction velocity error vN2Difference of vE13＝vE1-vE3Modulating laser gyro navigation inertial navigation 1 east direction velocity error v for single axis rotationE1And biaxial rotation modulation laser gyro navigation inertial navigation 3 east direction velocity error vE3Difference of vN13＝vN1-vN3Modulating laser gyro navigation inertial navigation 1 north velocity error v for single axis rotationN1And biaxial rotation modulation laser gyro navigation inertial navigation 3 north direction velocity error vN3Difference of (D), L12＝L1-L2Method for modulating 1 latitude error L of laser gyro navigation inertial navigation for single-axis rotation12-latitude error L of navigation inertial navigation of laser gyro modulated by double-axis rotation2A difference of (a)12＝λ1-λ2Method for modulating 1 longitude error lambda of laser gyro navigation inertial navigation for single-axis rotation1Laser gyro navigation inertial navigation 2 longitude error lambda modulated by double-axis rotation2Difference of (D), L13＝L1-L3Method for modulating 1 latitude error L of laser gyro navigation inertial navigation for single-axis rotation1Laser gyro navigation inertial navigation 3 latitude error L modulated by double-shaft rotation3A difference of (a)13＝λ1-λ3Method for modulating 1 longitude error lambda of laser gyro navigation inertial navigation for single-axis rotation1Laser gyro navigation inertial navigation 3 longitude error lambda modulated by double-axis rotation3The difference value of (a) to (b),x1、y1、z1respectively the gyro constant drift of the corresponding coordinate axis under the coordinate system of the single-axis rotation modulation laser gyro navigation inertial navigation 1 body,x2、y2、z2respectively the gyro constant drift of the corresponding coordinate axis under the biaxial rotation modulation laser gyro navigation inertial navigation 2 body coordinate system,x3、y3、z3respectively the gyro constant drift of the corresponding coordinate axis under the biaxial rotation modulation laser gyro navigation inertial navigation 3 body coordinate system,respectively, the accelerometer constant values of the corresponding horizontal coordinate axes of the single-axis rotation modulation laser gyro navigation inertial navigation 1 are zero offset,the accelerometer constant values of the corresponding horizontal coordinate axes of the biaxial rotation modulation laser gyro navigation inertial navigation system 2 are respectively zero offset,respectively, the accelerometer constant values of the corresponding horizontal coordinate axes of the biaxial rotation modulation laser gyro navigation inertial navigation 3 are zero offset, and the superscript T represents transposition;
step two: respectively establishing joint error state equations between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 2, and between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 3, wherein the joint error state equations are respectively
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>F</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>x</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>G</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>w</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>F</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>x</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>G</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>w</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
Wherein, the system state matrix is respectively:
<mrow> <msub> <mi>F</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mtable> <mtr> <mtd> <msub> <mi>F</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>3</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>4</mn> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>4</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>F</mi> <mn>5</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>6</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>7</mn> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>6</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>8</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>9</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>10</mn> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>6</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>4</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mn>.........................................</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>10</mn> <mo>&amp;times;</mo> <mn>17</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>F</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mtable> <mtr> <mtd> <msub> <mi>F</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>3</mn> </msub> </mtd> <mtd> <msub> <mover> <mi>F</mi> <mo>^</mo> </mover> <mn>4</mn> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>4</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>F</mi> <mn>5</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>6</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>7</mn> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>6</mn> </mrow> </msub> </mtd> <mtd> <msub> <mover> <mi>F</mi> <mo>^</mo> </mover> <mn>8</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>9</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>10</mn> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>6</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>4</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mn>.........................................</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>10</mn> <mo>&amp;times;</mo> <mn>17</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>F</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>v</mi> <mi>E</mi> </msub> <mi>tan</mi> <mi> </mi> <mi>L</mi> </mrow> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> </mfrac> <mo>+</mo> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>sin</mi> <mi> </mi> <mi>L</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>cos</mi> <mi> </mi> <mi>L</mi> <mo>-</mo> <mfrac> <msub> <mi>v</mi> <mi>E</mi> </msub> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mfrac> <mrow> <msub> <mi>v</mi> <mi>E</mi> </msub> <mi>tan</mi> <mi> </mi> <mi>L</mi> </mrow> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>sin</mi> <mi> </mi> <mi>L</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <msub> <mi>v</mi> <mi>N</mi> </msub> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>cos</mi> <mi> </mi> <mi>L</mi> <mo>+</mo> <mfrac> <msub> <mi>v</mi> <mi>E</mi> </msub> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mfrac> <msub> <mi>v</mi> <mi>N</mi> </msub> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>F</mi> <mn>2</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <mn>1</mn> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mi>tan</mi> <mi> </mi> <mi>L</mi> </mrow> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>F</mi> <mn>3</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>sin</mi> <mi> </mi> <mi>L</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>cos</mi> <mi> </mi> <mi>L</mi> <mo>+</mo> <mfrac> <msub> <mi>v</mi> <mi>E</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> <mo>)</mo> <msup> <mi>cos</mi> <mn>2</mn> </msup> <mi>L</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>F</mi> <mn>4</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>C</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </mrow> </mtd> <mtd> <msubsup> <mi>C</mi> <mrow> <mi>b</mi> <mn>2</mn> </mrow> <mi>n</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mover> <mi>F</mi> <mo>^</mo> </mover> <mn>4</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>C</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </mrow> </mtd> <mtd> <msubsup> <mi>C</mi> <mrow> <mi>b</mi> <mn>3</mn> </mrow> <mi>n</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>F</mi> <mn>5</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>f</mi> <mi>U</mi> </msub> </mrow> </mtd> <mtd> <msub> <mi>f</mi> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>f</mi> <mi>U</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>f</mi> <mi>E</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>F</mi> <mn>6</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mfrac> <mrow> <msub> <mi>v</mi> <mi>N</mi> </msub> <mi>tan</mi> <mi> </mi> <mi>L</mi> </mrow> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> </mfrac> </mtd> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>v</mi> <mi>E</mi> </msub> <mi>tan</mi> <mi> </mi> <mi>L</mi> </mrow> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> </mfrac> <mo>+</mo> <mn>2</mn> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>sin</mi> <mi> </mi> <mi>L</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>2</mn> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>sin</mi> <mi> </mi> <mi>L</mi> <mo>-</mo> <mn>2</mn> <mfrac> <mrow> <msub> <mi>v</mi> <mi>E</mi> </msub> <mi>tan</mi> <mi> </mi> <mi>L</mi> </mrow> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>F</mi> <mn>7</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mn>2</mn> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <msub> <mi>v</mi> <mi>N</mi> </msub> <mi>cos</mi> <mi> </mi> <mi>L</mi> <mo>+</mo> <mfrac> <mrow> <msub> <mi>v</mi> <mi>N</mi> </msub> <msub> <mi>v</mi> <mi>E</mi> </msub> </mrow> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> <mo>)</mo> </mrow> <msup> <mi>cos</mi> <mn>2</mn> </msup> <mi>L</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>2</mn> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <msub> <mi>v</mi> <mi>E</mi> </msub> <mi>cos</mi> <mi> </mi> <mi>L</mi> <mo>-</mo> <mfrac> <msubsup> <mi>v</mi> <mi>E</mi> <mn>2</mn> </msubsup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> <mo>)</mo> </mrow> <msup> <mi>cos</mi> <mn>2</mn> </msup> <mi>L</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>F</mi> <mn>8</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </mtd> <mtd> <mrow> <mo>-</mo> <msubsup> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>b</mi> <mn>2</mn> </mrow> <mi>n</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mover> <mi>F</mi> <mo>^</mo> </mover> <mn>8</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </mtd> <mtd> <mrow> <mo>-</mo> <msubsup> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>b</mi> <mn>3</mn> </mrow> <mi>n</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msubsup> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <mo>=</mo> <msubsup> <mi>MC</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <msup> <mi>M</mi> <mi>T</mi> </msup> <mo>,</mo> <msubsup> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>b</mi> <mn>2</mn> </mrow> <mi>n</mi> </msubsup> <mo>=</mo> <msubsup> <mi>MC</mi> <mrow> <mi>b</mi> <mn>2</mn> </mrow> <mi>n</mi> </msubsup> <msup> <mi>M</mi> <mi>T</mi> </msup> <mo>,</mo> <msubsup> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>b</mi> <mn>3</mn> </mrow> <mi>n</mi> </msubsup> <mo>=</mo> <msubsup> <mi>MC</mi> <mrow> <mi>b</mi> <mn>3</mn> </mrow> <mi>n</mi> </msubsup> <msup> <mi>M</mi> <mi>T</mi> </msup> <mo>,</mo> <mi>M</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>F</mi> <mn>9</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mn>1</mn> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>+</mo> <mi>h</mi> </mrow> </mfrac> </mtd> </mtr> <mtr> <mtd> <mfrac> <mn>1</mn> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> <mo>)</mo> <mi>cos</mi> <mi> </mi> <mi>L</mi> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>F</mi> <mn>10</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <msub> <mi>v</mi> <mi>E</mi> </msub> <mi>tan</mi> <mi> </mi> <mi>L</mi> </mrow> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <mi>h</mi> <mo>)</mo> <mi>cos</mi> <mi> </mi> <mi>L</mi> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
vE、vNeast-direction speed, north-direction speed, omega of naval vesselieIs the rotational angular velocity of the earth, L is the latitude position of the naval vessel, h is the height of the naval vessel, RE、RNIs Mao Yue circle and meridian circle yeast respectivelyRadius of curvature, fE、fN、fUAre respectively east, north and sky specific force values,respectively are attitude matrixes of a single-axis rotation modulation laser gyro navigation inertial navigation system 1 and double-axis rotation modulation laser gyro navigation inertial navigation systems 2 and 3,respectively is a submatrix formed by the first two rows and the first two columns of the attitude matrixes of a single-axis rotation modulation laser gyro navigation inertial navigation 1 and double-axis rotation modulation laser gyro navigation inertial navigation 2 and 3 respectively, and 0i×jA zero matrix representing i rows and j columns;
the system noise driving matrix is respectively:
<mrow> <msub> <mi>G</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>C</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </mrow> </mtd> <mtd> <msubsup> <mi>C</mi> <mrow> <mi>b</mi> <mn>2</mn> </mrow> <mi>n</mi> </msubsup> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>4</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>6</mn> </mrow> </msub> </mtd> <mtd> <msubsup> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </mtd> <mtd> <mrow> <mo>-</mo> <msubsup> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>b</mi> <mn>2</mn> </mrow> <mi>n</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mn>............................</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>12</mn> <mo>&amp;times;</mo> <mn>10</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>G</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>C</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </mrow> </mtd> <mtd> <msubsup> <mi>C</mi> <mrow> <mi>b</mi> <mn>3</mn> </mrow> <mi>n</mi> </msubsup> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>4</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>6</mn> </mrow> </msub> </mtd> <mtd> <msubsup> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </mtd> <mtd> <mrow> <mo>-</mo> <msubsup> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>b</mi> <mn>3</mn> </mrow> <mi>n</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mn>............................</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>12</mn> <mo>&amp;times;</mo> <mn>10</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
the system noise is:
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>w</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>w</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>y</mi> <mn>1</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mn>2</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>y</mi> <mn>2</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mn>2</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>y</mi> <mn>1</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>x</mi> <mn>2</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>y</mi> <mn>2</mn> </mrow> </msub> </msub> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>w</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>w</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>y</mi> <mn>1</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mn>3</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>y</mi> <mn>3</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mn>3</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>y</mi> <mn>1</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>x</mi> <mn>3</mn> </mrow> </msub> </msub> </mtd> <mtd> <msub> <mi>w</mi> <msub> <mo>&amp;dtri;</mo> <mrow> <mi>y</mi> <mn>3</mn> </mrow> </msub> </msub> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>2
respectively modulating the gyro noise of corresponding coordinate axes under a body coordinate system of the laser gyro navigation inertial navigation system 1 by single-axis rotation,respectively modulating the gyro noise of corresponding coordinate axes under a 2-body coordinate system of the laser gyro navigation inertial navigation system by biaxial rotation,are respectively a double axisThe gyro noise of the corresponding coordinate axis under the coordinate system of the laser gyro navigation inertial navigation 3 body is modulated in a rotating way,respectively are accelerometer noises of corresponding horizontal coordinate axes under a uniaxial rotation modulation laser gyro navigation inertial navigation 1 body coordinate system,respectively modulating the accelerometer noise of corresponding horizontal coordinate axes under a navigation inertial navigation system 2 body coordinate system of the laser gyro by biaxial rotation,respectively modulating the accelerometer noise of the corresponding horizontal coordinate axis under a navigation inertial navigation system 3 body coordinate system of the laser gyroscope in a biaxial rotation manner;
step three: respectively establishing observation equations between a single-axis rotation modulation laser gyro navigation inertial navigation system 1 and a double-axis rotation modulation laser gyro navigation inertial navigation system 2, between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and a double-axis rotation modulation laser gyro navigation inertial navigation system 3, wherein the observed quantities are the speed difference and the position difference between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation modulation laser gyro navigation inertial navigation system 2 and 3 after the lever arm effect is deducted, and the observation equations are respectively the speed difference and the position difference between the single-axis rotation modulation laser gyro navigation inertial navigation system 1 and the double-axis rotation
z12(t)＝Hx12(t)+v(t),z13(t)＝Hx13(t)+v(t) (12)
Wherein,
z12(t)＝[vE12vN12L12λ12]T,z13(t)＝[vE13vN13L13λ13]T(13)
v (t) is the observation matrix, and v (t) is the observation noise;
z12(t)、z13(t) shows uniaxial rotation modulation laser gyroThe observation quantity between the sea inertial navigation 1 and the biaxial rotation modulation laser gyro navigation inertial navigation 2 and 3,shows the east output speed of the single-axis rotation modulation laser gyro navigation inertial navigation system 1East direction output speed of laser gyro navigation inertial navigation system 2 is modulated with double-shaft rotationThe difference value of (a) to (b),representing the north output speed of the single-axis rotation modulation laser gyro navigation inertial navigation system 1And the double-shaft rotation modulation laser gyro navigation inertial navigation 2 northbound output speedThe difference value of (a) to (b),shows the east output speed of the single-axis rotation modulation laser gyro navigation inertial navigation system 1East output speed of laser gyro navigation inertial navigation 3 is modulated with double-shaft rotationThe difference value of (a) to (b),representing the north output speed of the single-axis rotation modulation laser gyro navigation inertial navigation system 1And the double-shaft rotation modulation laser gyro navigation inertial navigation 3 northbound output speedThe difference value of (a) to (b),representing the output latitude of the single-axis rotation modulation laser gyro navigation inertial navigation system 1Output latitude of laser gyro navigation inertial navigation 2 modulated by double-shaft rotationThe difference value of (a) to (b),representing the output longitude of a single-axis rotation modulation laser gyro navigation inertial navigation system 1Output longitude of laser gyro navigation inertial navigation system 2 modulated by double-shaft rotationThe difference value of (a) to (b),representing the output latitude of the single-axis rotation modulation laser gyro navigation inertial navigation system 1And the output latitude of the biaxial rotation modulation laser gyro navigation inertial navigation 3The difference value of (a) to (b),representing the output longitude of a single-axis rotation modulation laser gyro navigation inertial navigation system 1Output longitude of laser gyro navigation inertial navigation system 3 modulated by double-shaft rotationDifference of (A) to (B), I2×2Representing a second order identity matrix;
step four: determining the influence of system noise on the drift estimation value of the single-axis rotation modulation laser gyroscope navigation inertial navigation azimuth gyroscope, and realizing the following steps:
1) determining a steady state estimation error covariance matrix for the system state corresponding to the joint error state Kalman filter
Deducting the influence of lever arm errors caused by installation relation, the theoretical value of the speed difference and the position difference between the single-axis rotation modulation laser gyro navigation inertial navigation 1 and the double-axis rotation modulation laser gyro navigation inertial navigation 2 and 3 is 0, which can be approximated to be free of observation noise, and the steady state estimation error covariance matrix P of the corresponding system state of the joint error state Kalman filter meets the requirement of no observation noise
P＝(I-KH)FPFT(I-KH)T+(I-KH)GQGT(I-KH)T(14)
K is Kalman filtering gain, Q is a set value of a Kalman filter system noise covariance matrix, F is a system state matrix, H is an observation matrix, G is a system noise matrix, and I is an identity matrix;
2) determining a true system noise covariance matrixThe relation between the set value of the noise covariance matrix of the Kalman filter system is
Wherein alpha is an unknown scalar and represents the difference between the real noise covariance matrix and a set value; if alpha is more than 0, the real system noise covariance matrix is larger than the set value; if alpha is less than 0, the real system noise covariance matrix is smaller than the set value; if alpha is 0, the real system noise covariance matrix is equal to the set value;
3) determining a steady state estimation error covariance matrix for the system state corresponding to the true system noise covariance matrixIs composed of
<mrow> <mover> <mi>P</mi> <mo>~</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mi>I</mi> <mo>-</mo> <mi>K</mi> <mi>H</mi> <mo>)</mo> </mrow> <mi>F</mi> <mover> <mi>P</mi> <mo>~</mo> </mover> <msup> <mi>F</mi> <mi>T</mi> </msup> <msup> <mrow> <mo>(</mo> <mi>I</mi> <mo>-</mo> <mi>K</mi> <mi>H</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <mrow> <mo>(</mo> <mi>I</mi> <mo>-</mo> <mi>K</mi> <mi>H</mi> <mo>)</mo> </mrow> <mi>G</mi> <mover> <mi>Q</mi> <mo>~</mo> </mover> <msup> <mi>G</mi> <mi>T</mi> </msup> <msup> <mrow> <mo>(</mo> <mi>I</mi> <mo>-</mo> <mi>K</mi> <mi>H</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>
4) Determining a change Δ P in the state estimation error covariance caused by an inconsistency between the true noise covariance matrix and the Kalman filter system noise covariance matrix set point as
<mrow> <mi>&amp;Delta;</mi> <mi>P</mi> <mo>=</mo> <mover> <mi>P</mi> <mo>~</mo> </mover> <mo>-</mo> <mi>P</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>I</mi> <mo>-</mo> <mi>K</mi> <mi>H</mi> <mo>)</mo> </mrow> <msup> <mi>F&amp;Delta;PF</mi> <mi>T</mi> </msup> <msup> <mrow> <mo>(</mo> <mi>I</mi> <mo>-</mo> <mi>K</mi> <mi>H</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <mi>&amp;alpha;</mi> <mrow> <mo>(</mo> <mi>I</mi> <mo>-</mo> <mi>K</mi> <mi>H</mi> <mo>)</mo> </mrow> <msup> <mi>GQG</mi> <mi>T</mi> </msup> <msup> <mrow> <mo>(</mo> <mi>I</mi> <mo>-</mo> <mi>K</mi> <mi>H</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>=</mo> <mi>&amp;alpha;</mi> <mi>P</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>
5) Determining the influence of system noise on the drift estimation value of the single-axis rotation modulation laser gyro navigation inertial navigation azimuth gyro
According to the formula (16) in the step 4), if the real system noise covariance matrix is larger than the set value, that is, α is larger than 0, the variance of the real system state estimation error is larger than the variance of the nominal system state estimation error; if the real system noise covariance matrix is smaller than the nominal value, namely alpha is less than 0, the variance of the real system state estimation error is less than the variance of the nominal system state estimation error; for a steady-state Kalman filter, the smaller the variance of system state estimation errors is, the smaller the standard deviation of corresponding system state estimation values is, and the smaller the standard deviation of corresponding single-axis rotation modulation laser gyro navigation inertial navigation 1 azimuth gyro drift estimation values is;
step five: performing Kalman filtering according to a system state equation and an observation equation between a single-axis rotation modulation laser gyro navigation inertial navigation device 1 and double-axis rotation modulation laser gyro navigation inertial navigation devices 2 and 3 respectively, estimating respective system states, finishing online estimation of relative performance between the double-axis rotation modulation laser gyro navigation inertial navigation devices 2 and 3 by taking a standard difference of azimuth gyro drift estimation values of the single-axis rotation modulation laser gyro navigation inertial navigation device 1 after two Kalman filters are stabilized as an evaluation index, wherein random errors of the double-axis rotation modulation laser gyro navigation inertial navigation devices corresponding to the filters with smaller standard differences of the azimuth gyro drift estimation values of the single-axis rotation modulation laser gyro navigation inertial navigation device 1 in the same time period are smaller, and the positioning precision is higher;
azimuth gyro drift estimation value standard deviation sigma of single-axis rotation modulation laser gyro navigation inertial navigation 1 obtained by Kalman filter estimation composed of single-axis rotation modulation laser gyro navigation inertial navigation 1 and double-axis rotation modulation laser gyro navigation inertial navigation 22(z1) The standard deviation sigma of the azimuth gyro drift estimation value of the single-axis rotation modulation laser gyro navigation inertial navigation 1 is obtained by the Kalman filter estimation composed of the single-axis rotation modulation laser gyro navigation inertial navigation 1 and the double-axis rotation modulation laser gyro navigation inertial navigation 33(z1) Respectively as follows:
<mrow> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>&amp;epsiv;</mi> <mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;mu;</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> </msub> </msub> <mo>)</mo> </mrow> </mrow> </msqrt> <mo>,</mo> <msub> <mi>&amp;sigma;</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>&amp;epsiv;</mi> <mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;mu;</mi> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> </msub> </msub> <mo>)</mo> </mrow> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>
calculating the standard deviation of the single-axis rotation modulation laser gyro navigation inertial navigation 1 azimuth gyro drift estimation value once every fixed time length, and comparing the random error of the two filters corresponding to the double-axis rotation modulation laser gyro navigation inertial navigation by taking the standard deviation as an index; wherein N is the number of the azimuth gyro drift estimated values of the uniaxial rotation modulation laser gyro navigation inertial navigation 1 in the time period,the mean value of the azimuth gyro drift estimated values of the single-axis rotation modulation laser gyro navigation inertial navigation 1 in the time period is obtained;
if σ2(z1)＜σ3(z1) The random error of the double-shaft rotation modulation laser gyro navigation inertial navigation 2 is smaller, and the positioning is realizedThe precision is higher, and a double-shaft rotation modulation laser gyro navigation inertial navigation system 2 is selected as a main inertial navigation system;
if σ2(z1)＞σ3(z1) If so, the random error of the biaxial rotation modulation laser gyro navigation inertial navigation system 3 is smaller, the positioning precision is higher, and the biaxial rotation modulation laser gyro navigation inertial navigation system 3 is selected as a main inertial navigation system;
step six: using the uniaxial rotation modulation laser gyroscope navigation inertial navigation 1 azimuth gyroscope drift with smaller standard deviation estimated in the fifth step as a final estimation value, and performing prediction compensation on the deterministic long-term positioning error caused by the final estimation value, wherein the compensation mode is output correction;
the prediction compensation step of the deterministic long-term positioning error caused by the drift of the azimuth gyroscope of the single-axis rotation modulation laser gyroscope navigation inertial navigation 1 comprises the following steps:
1) determining the error state x of the single-axis rotation modulation laser gyro navigation inertial navigation system 11(t) is
x1(t)＝[φE1φN1φU1vE1vN1L1λ1]T(18)
Wherein phi isE1For the single-axis rotation modulation of the east attitude error, phi, of the laser gyro navigation inertial navigation system 1N1For single-axis rotation modulation of the north attitude error, phi, of the laser gyro navigation inertial navigation system 1U1For single-axis rotation modulation of the attitude error, v, of the laser gyro navigation inertial navigation system 1E1For the uniaxial rotation modulation of the east velocity error, v, of the laser gyro navigation inertial navigation 1N1For the single-axis rotation modulation of the north velocity error, L, of the laser gyro navigation inertial navigation system 11For single-axis rotation modulation of latitude error, lambda, of laser gyro navigation inertial navigation 11The longitude error of the laser gyro navigation inertial navigation system 1 is modulated by single-axis rotation;
2) determining the external input quantity u formed by gyro drift and accelerometer zero offset in the error state equation of the single-axis rotation modulation laser gyro navigation inertial navigation 11(t) is
3) Constructing an error state equation of the single-axis rotation modulation laser gyro navigation inertial navigation 1
<mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>A</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>B</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>G</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>w</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow>
Wherein,
<mrow> <msub> <mi>A</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>F</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>F</mi> <mn>5</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>6</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>7</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>9</mn> </msub> </mtd> <mtd> <msub> <mi>F</mi> <mn>10</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>B</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>C</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </mrow> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msubsup> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>G</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>C</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </mrow> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msubsup> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>b</mi> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow>
A1(t) is the system state matrix, B1(t) is an external input matrix, G1(t) is a system noise matrix;
the method comprises the following steps of modulating system noise consisting of gyro noise and accelerometer noise of the laser gyro navigation inertial navigation system 1 for single-axis rotation;
4) obtaining an error state prediction equation of a discretized single-axis rotation modulation laser gyro navigation inertial navigation system 1 from an error state equation (19)
<mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;Phi;</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&amp;Gamma;</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>u</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> </mrow>
Wherein,is the system state x1Discrete amount of (t), phi1(k) Is a system state matrix A1(t) a discrete matrix of the plurality of discrete matrices,1(k) for external input matrix B1(t) a discrete matrix of the plurality of discrete matrices,for external input u1(t), k +1 are discretization time, initial time
5) And carrying out prediction compensation on the deterministic long-term positioning error caused by the drift of the azimuth gyroscope of the single-axis rotation modulation laser gyroscope navigation inertial navigation 1 according to an error state prediction equation by Kalman filtering, wherein the compensation mode is output correction.
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