CN114442076A - Ultra-short baseline installation angle deviation combined adjustment calibration method based on difference technology - Google Patents

Ultra-short baseline installation angle deviation combined adjustment calibration method based on difference technology Download PDF

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CN114442076A
CN114442076A CN202210031291.5A CN202210031291A CN114442076A CN 114442076 A CN114442076 A CN 114442076A CN 202210031291 A CN202210031291 A CN 202210031291A CN 114442076 A CN114442076 A CN 114442076A
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angle deviation
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刘慧敏
杨源
单瑞
周吉祥
杜凯
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Qingdao Institute of Marine Geology
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Abstract

The invention relates to a calibration technology of installation angle deviation of an ultra-short baseline positioning system, in particular to a combined adjustment calibration method of the installation angle deviation of the ultra-short baseline based on a difference technology. The method comprises the following steps: laying a seabed ultra-short baseline calibration beacon, sailing a measuring ship provided with an ultra-short baseline transducer along a calibration track, and synchronously acquiring and recording data; constructing a Gaussian Markov model of the combined calibration model by using the calibration data group; solving a floating point solution of a direction rotation matrix of the installation angle deviation based on the combined adjustment model; constructing an inter-epoch difference equation, and solving a direction cosine matrix floating point solution of the angle installation deviation; orthogonalizing a non-orthogonal directional cosine matrix differential floating-point solution; iteratively solving an optimal solution of the deviation of the installation angle; more accurate coordinates of the calibration beacon and a covariance matrix of the calibration beacon are calculated. The calibration precision of the installation angle deviation of the ultra-short baseline is improved, and the calculation precision of the seabed calibration beacon position and the calibration precision of the installation angle deviation are effectively improved.

Description

Ultra-short baseline installation angle deviation combined adjustment calibration method based on difference technology
Technical Field
The invention relates to a calibration technology of installation angle deviation of an ultra-short baseline positioning system, in particular to a combined adjustment calibration method of the installation angle deviation of the ultra-short baseline based on a difference technology.
Background
In the existing Ultra-Short Baseline (abbreviated as USBL, the same below) calibration scheme, firstly, the geodetic coordinates of the calibration beacon at the sea bottom are obtained through the ranging observation value of the symmetric flight path, then the geodetic coordinates of the calibration beacon are brought into a calibration equation to be calibrated through an iteration method, the method cannot fully utilize the azimuth data of the Ultra-Short Baseline to solve, and the positioning accuracy is limited.
When the sound velocity error in the calibration process is processed, the existing method eliminates the horizontal influence through a symmetrical track, and solves the installation angle deviation by constructing an iterative adjustment submarine calibration beacon vertical direction to minimize the objective function. The method has the main problems that the calibration tracks are difficult to ensure complete symmetry, so that the horizontal positioning precision is influenced, and the final installation angle deviation is biased.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides an ultrashort baseline installation angle deviation joint adjustment calibration method based on a difference technology, realizes floating solution and fixed solution calculation of an installation angle deviation cosine matrix based on a matrix Crornike product operation and a Levenberg-Marquardt method, improves the calibration precision of the installation angle deviation of the ultrashort baseline under the condition of sound velocity error, and effectively improves the calculation precision of a submarine calibration beacon position and the calibration precision of the installation angle deviation.
The technical scheme of the invention is as follows: a combined adjustment calibration method for ultra-short baseline installation angle deviation based on a difference technology comprises the following steps:
s1, laying a seabed ultra-short baseline calibration beacon, sailing a measuring ship provided with an ultra-short baseline transducer along a calibration track, and synchronously acquiring and recording differential satellite positioning data, ship course attitude data and acoustic relative positioning data;
s2, constructing a Gaussian Markov model of the combined calibration model by using the calibration data group;
s3, solving a floating point solution of a direction rotation matrix of the installation angle deviation based on the combined adjustment model;
s4, constructing an inter-epoch difference equation based on a joint adjustment model, and solving a direction cosine matrix floating point solution of the angle installation deviation;
s5, carrying out differential floating point solution on non-orthogonal directional cosine matrix
Figure BDA0003466564000000011
Carrying out orthogonalization;
s6, based on a Levenberg-Marquardt iteration method, iteratively calculating an optimal solution of the deviation of the installation angle by using a direction cosine matrix covariance matrix, an angle deviation Euler angle, a floating point solution and a fixed solution;
and S7, calculating more accurate coordinates of the calibration beacon and a covariance matrix of the calibration beacon based on the optimal solution of the installation angle deviation obtained in the step S6.
In the present invention, step S2 specifically includes the following calculation method:
taking the ZYX coordinate system as an example, let three angular deviation components between the hull coordinate system and the USBL coordinate system be: phi theta psi]Wherein phi is the course angle deviation, theta is the longitudinal rocking angle deviation, psi is the transverse rocking angle deviation, and a direction cosine matrix is set
Figure BDA0003466564000000021
Comprises the following steps:
Figure BDA0003466564000000022
wherein s isα＝sin(α)，cα＝cos(α)；
The position of the GNSS at the time k in a navigation coordinate system is set as
Figure BDA0003466564000000023
The USBL has the coordinates in the navigation coordinate system of
Figure BDA0003466564000000024
Fixed mounting distance bias between GNSS and USBLIs Δ X ═ Δ X Δ y Δ z]T，
Figure BDA0003466564000000025
The acoustic relative position of the USBL with respect to the seafloor calibration beacon, that is, the acoustic relative positioning data collected in step S1, can be obtained as follows:
Figure BDA0003466564000000026
wherein
Figure BDA0003466564000000027
B represents a hull coordinate system and n represents a navigation coordinate system for the attitude rotation matrix at the time k acquired in the step S1;
setting the USBL to collect m pairs of calibration data, and constructing the following Gaussian Markov model based on all observation data:
Figure BDA0003466564000000028
wherein: e (-) represents a mathematical expectation; y is 3 xm observation value array, Y ═ Y1 y2 … ym]，
Figure BDA0003466564000000029
pBRepresenting coordinates of the seafloor calibration beacon in a navigation coordinate system; a is a coefficient array of 3m multiplied by 3,
Figure BDA00034665640000000210
PUis a 3 × m matrix, and
Figure BDA00034665640000000211
d (-) represents the mathematical variance; qYA covariance matrix of 3m × 3 m; vec (-) denotes the stretch vector of the matrix.
In step S3, the method specifically includes the following calculation method:
converting the parameter estimation problem of the Gaussian Markov model obtained in the step S2 into:
Figure BDA0003466564000000031
wherein the content of the first and second substances,
Figure BDA0003466564000000032
SO (3) is a direction rotation matrix,
Figure BDA0003466564000000033
and simultaneously calculating the position of the calibration beacon and the floating solution N of the direction cosine matrix:
Figure BDA0003466564000000034
wherein, I3The unit matrix is a main diagonal element 1, and the rest are 0;
Figure BDA0003466564000000035
a kronecker product representing the matrix;
covariance matrix for calculating floating point solution N
Figure BDA0003466564000000036
Wherein the content of the first and second substances,
Figure BDA0003466564000000037
a location covariance matrix representing the calibration beacon,
Figure BDA0003466564000000038
a cross-covariance matrix representing the calibration beacon and the direction cosine matrix,
Figure BDA0003466564000000039
a covariance matrix representing a directional cosine matrix.
In step S4, the method specifically includes the following calculation method:
and (3) obtaining the following result by making the difference between the observation equations at the k moment and the j moment:
Figure BDA00034665640000000310
at this time, m/2 single difference observation equations are constructed to obtain the following Gaussian Markov model:
Figure BDA00034665640000000311
wherein, the delta Y is an observation value array of 3 Xm/2; and Δ Y ═ Δ Y1,m/2+1 Δy2,m/2+2 … Δym/2,m](ii) a Delta A is a parameter matrix of 3m/2 multiplied by 3,
Figure BDA00034665640000000312
ΔPUis a matrix of 3 Xm/2, and
Figure BDA00034665640000000313
QΔYa covariance matrix of 3m/2 × 3 m/2;
converting the parameter estimation problem of the Gaussian Markov model into:
Figure BDA00034665640000000314
and resolving the location of the calibration beacon
Figure BDA0003466564000000041
Differential floating point solution of sum direction cosine matrix
Figure BDA0003466564000000042
Figure BDA0003466564000000043
Wherein, is Δ QYIs a covariance matrix;
calculating a covariance matrix of Δ N
Figure BDA0003466564000000044
In step S5, the method specifically includes the following calculation methods:
orthogonal matrix for calculating direction cosine matrix differential floating point solution
Figure BDA0003466564000000045
Figure BDA0003466564000000046
Computing orthogonal matrices
Figure BDA0003466564000000047
Corresponding Euler angle
Figure BDA0003466564000000048
In step S6, the method specifically includes the following calculation method:
jacobian matrix for calculating direction cosine matrix
Figure BDA0003466564000000049
Figure BDA0003466564000000051
Wherein s isαI＝sin(αI)，cαI＝cos(αI)；ΘIFor angular deviation of mounting, thetaI＝[φI θI ψI]；
Calculating an observed value vector
Figure BDA0003466564000000052
Figure BDA00034665640000000512
Calculating the installation angle deviation increment delta thetaI
Figure BDA0003466564000000053
Wherein, λ is a known damping matrix, and is self-adaptively adjusted in an iterative process;
and iteratively calculating the angle installation deviation, and outputting an optimal solution of the angle installation deviation.
In step S6, the iterative calculation of the angular installation deviation specifically includes the following iterative processes:
s6.1, selecting iteration termination parameter mu1And mu2Damping factor λ and damping scale factor η
S6.2. according to input
Figure BDA0003466564000000054
Calculated by equation (12)
Figure BDA0003466564000000055
Calculation of theta by equation (13)I。
S6.3, calculating the Jacobian matrix by the formula (14)
Figure BDA0003466564000000056
Calculation of an observed value vector by equation (15)
Figure BDA0003466564000000057
S6.4, calculating the mounting angle deviation increment delta theta according to the formula (16)I。
S6.5, carrying out iteration judgment:
if it is not
Figure BDA0003466564000000058
Then λk+1＝λkEta, and the calculation is continued from the step S6.3 again;
otherwise, if
Figure BDA0003466564000000059
And | | | δ ΘI||2≤μ1At this point, the iteration is stopped;
otherwise, if
Figure BDA00034665640000000510
And | | | δ ΘI||2≥μ1Then λk+1＝λkEta, and the calculation is continued from the step S6.3 again;
s6.6, outputting the optimal solution of the installation angle deviation after the iteration condition in the step S6.5 is met
Figure BDA00034665640000000511
In step S7, the coordinate position of the calibration beacon is calculated based on the direction cosine matrix of the installation angle deviation
Figure BDA0003466564000000061
Computing conditional covariance matrices for calibration beacons
Figure BDA0003466564000000062
Thereby obtaining the covariance matrix of the seabed calibration beacon coordinate and reflecting the precision of the seabed coordinate.
The invention has the beneficial effects that:
(1) in terms of calibration accuracy:
according to the method, on the resolving model, the correction of the angle installation deviation with extremely high precision can be realized, the combined model brings the azimuth information of the combined model into the calculation of the calibration beacon position, so that the beacon coordinate and the installation angle deviation cosine matrix can be estimated simultaneously, the model is closer to the actual calibration condition, and after the orthogonal optimal solution of the cosine matrix is obtained based on the LM method, the theoretical precision can reach one thousandth. The calibration precision obtained by the method is consistent with the APOS software precision of foreign Corsberg company through actual measurement experiment verification.
(2) Theoretical scalability aspects:
the model provided by the application has compatibility, although the operation of the kronecker product enables most of non-mathematical professionals in the field to abandon the joint method adjustment model, the method can properly increase or delete the calibration parameters according to the actual situation, so that the method is flexibly applied to the commercialized calibration software, and the calibration accuracy can be effectively evaluated.
In conclusion, the method constructs a floating-point solution of the ultra-short baseline installation angle deviation non-orthogonal cosine matrix based on the difference technology, and utilizes Levenberg-Marquardt to solve an orthogonal optimal cosine matrix fixed solution based on the covariance matrix, so that the calculation precision of the seabed calibration beacon position and the calibration precision of the installation angle deviation can be effectively improved.
Drawings
FIG. 1 is a schematic line drawing of ultra-short baseline calibration based on static mode;
FIG. 2 is a schematic line drawing of ultra-short baseline calibration based on dynamic mode;
fig. 3 is a flowchart for iteratively solving the installation angle deviation based on the LM iteration method.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
In the following description, specific details are set forth in order to provide a thorough understanding of the present invention. The invention can be implemented in a number of ways different from those described herein and similar generalizations can be made by those skilled in the art without departing from the spirit of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.
The ultrashort baseline installation angle deviation combined adjustment calibration method based on the difference technology comprises the following steps.
Firstly, a submarine ultrashort baseline calibration beacon is laid, a measuring ship provided with an ultrashort baseline transducer sails along a calibration track, and differential Satellite positioning (GNSS, the same below) data, ship course attitude data and acoustic relative positioning data are synchronously acquired and recorded.
In the application, the measuring ship adopts two modes for data acquisition through a dynamic positioning system, namely fixed-point data acquisition based on a static mode and fixed-point data acquisition based on a dynamic mode. As shown in fig. 1, the data acquisition is based on a static mode, the static calibration positions are located at four positions right above the beacon and four calibration points at the fixed position with equal water depth, and the number of the data acquired in each group is the same. As shown in fig. 2, the data collection is based on a dynamic mode, which is based on the straight course of the ship, and the track planning can be generally divided into four-azimuth and eight-azimuth straight line calibration modes, and data are collected through symmetrical tracks.
And then preprocessing the acquired data, such as time unification, abnormal observation value elimination and the like. In the embodiment, the recorded data is preprocessed, and the data acquired by a plurality of sensors can be subjected to time unification by a Lagrange difference method; and the elevation of the satellite positioning antenna can be smoothed by adopting an empirical mode decomposition technology, and an abnormal observation value is eliminated.
And secondly, constructing a Gaussian Markov model of the combined calibration model by using the calibration data group.
Taking the ZYX coordinate system as an example, let three angular deviation components between the hull coordinate system and the USBL coordinate system be: phi theta psi]Wherein phi is the course angle deviation, theta is the longitudinal rocking angle deviation, psi is the transverse rocking angle deviation, and a direction cosine matrix is set
Figure BDA0003466564000000071
Comprises the following steps:
Figure BDA0003466564000000072
wherein s isα＝sin(α)，cα＝cos(α)。
The position of the GNSS at the time k in a navigation coordinate system is set as
Figure BDA0003466564000000073
The USBL has the coordinates in the navigation coordinate system of
Figure BDA0003466564000000074
The fixed mounting distance deviation between the GNSS and the USBL is Δ X ═ Δ X Δ y Δ z]TAnd the measurement can be obtained by a laser range finder or a ship pattern.
Figure BDA0003466564000000075
And calibrating the acoustic relative position of the USBL relative to the seabed, namely obtaining the acoustic relative positioning data acquired in the first step. At this point it is possible to obtain:
Figure BDA0003466564000000076
wherein
Figure BDA0003466564000000077
B represents a ship body coordinate system and n represents a navigation coordinate system for the course attitude data acquired in the first step.
If the USBL is set to collect m pairs of calibration data, based on all observation data, the following Gaussian Markov model can be constructed:
Figure BDA0003466564000000081
wherein: e (-) represents a mathematical expectation; y is 3 xm observation value array, Y ═ Y1 y2 … ym]，
Figure BDA0003466564000000082
pBRepresenting subsea calibration beacons in a navigation coordinate systemThe coordinates of (a); a is a coefficient array of 3m multiplied by 3,
Figure BDA0003466564000000083
PUis a 3 × m matrix, and
Figure BDA0003466564000000084
d (-) represents the mathematical variance; qYA covariance matrix of 3m × 3m, which can be set according to experience or signal-to-noise ratio; vec (-) denotes the stretch vector of the matrix.
And thirdly, solving a floating point solution of the direction rotation matrix of the installation angle deviation based on the combined adjustment model.
Converting the parameter estimation problem of the Gaussian Markov model into:
Figure BDA0003466564000000085
wherein the content of the first and second substances,
Figure BDA0003466564000000086
SO (3) is a direction rotation matrix,
Figure BDA0003466564000000087
the estimation problem cannot be solved directly by the least square method due to the existence of the direction cosine matrix.
And simultaneously calculating the position of the calibration beacon and the floating solution N of the direction cosine matrix:
Figure BDA0003466564000000088
wherein, I3The unit matrix is a main diagonal element 1, and the rest are 0;
Figure BDA0003466564000000089
the kronecker product of the matrix is represented.
Covariance matrix for calculating floating point solution N
Figure BDA00034665640000000810
Wherein the content of the first and second substances,
Figure BDA00034665640000000811
a position covariance matrix of the calibration beacon is represented,
Figure BDA00034665640000000812
a cross-covariance matrix representing the calibration beacon and the direction cosine matrix,
Figure BDA00034665640000000813
a covariance matrix representing a directional cosine matrix.
And fourthly, constructing a difference equation between epochs based on the joint adjustment model, and solving a direction cosine matrix floating point solution of the angle installation deviation.
After the observation equations at the time k and j are differed, the following can be obtained:
Figure BDA0003466564000000091
at this time, m/2 single-difference observation equations can be constructed, so that the following Gaussian Markov model is obtained:
Figure BDA0003466564000000092
wherein, the delta Y is an observation value array of 3 Xm/2; and Δ Y ═ Δ Y1,m/2+1 Δy2,m/2+2 … Δym/2,m](ii) a Delta A is a parameter matrix of 3m/2 multiplied by 3,
Figure BDA0003466564000000093
ΔPUis a matrix of 3 Xm/2, and
Figure BDA0003466564000000094
QΔYis a covariance matrix of 3m/2 × 3 m/2.
Converting the parameter estimation problem of the Gaussian Markov model into:
Figure BDA0003466564000000095
and resolving a differential floating point solution delta N of the position and direction cosine matrix of the calibration beacon:
Figure BDA0003466564000000096
wherein, is Δ QYThe covariance matrix can be set empirically or by the signal-to-noise ratio.
Calculating covariance matrix of Δ N
Figure BDA0003466564000000097
Fifthly, carrying out differential floating point solution on the non-orthogonal directional cosine matrix
Figure BDA0003466564000000098
And performing orthogonalization.
Orthogonal matrix for calculating direction cosine matrix differential floating point solution
Figure BDA0003466564000000099
Figure BDA0003466564000000101
Computing orthogonal matrices
Figure BDA0003466564000000102
Corresponding Euler angle
Figure BDA0003466564000000103
And sixthly, iteratively calculating an optimal solution of the deviation of the installation angle by using a direction cosine matrix covariance matrix, an angle deviation Euler angle, a floating solution and a fixed solution based on a Levenberg-Marquardt iterative method.
Jacobian matrix for calculating direction cosine matrix
Figure BDA0003466564000000104
Figure BDA0003466564000000105
Wherein s isαI＝sin(αI)，cαI＝cos(αI)；ΘIFor angular deviation of mounting, thetaI＝[φI θI ψI]。
Calculating an observed value vector
Figure BDA0003466564000000106
Figure BDA0003466564000000107
Calculating the installation angle deviation increment delta thetaI
Figure BDA0003466564000000108
Wherein λ is a known damping matrix, and is adaptively adjusted in an iterative process.
Next, the angular installation deviation is iteratively solved, and a specific iterative flow is as follows.
(one) selecting an iteration termination parameter mu1And mu2A damping factor λ and a damping scale factor η.
Based on input
Figure BDA0003466564000000111
Calculated by equation (12)
Figure BDA0003466564000000112
Calculation of theta by equation (13)I。
(III) calculation of Jacobian matrix by equation (14)
Figure BDA0003466564000000113
Calculation of an observed value vector by equation (15)
Figure BDA0003466564000000114
Fourthly, calculating the deviation increment delta theta of the installation angle according to the formula (16)I。
(V) carrying out iterative judgment:
if it is not
Figure BDA0003466564000000115
Then λk+1＝λkEta, and continuing to calculate from the step (three) again;
otherwise, if
Figure BDA0003466564000000116
And | | | δ ΘI||2≤μ1The iteration is stopped at this point.
Otherwise, if
Figure BDA0003466564000000117
And | | | δ ΘI||2≥μ1Then λ isk+1＝λkAnd/eta, and the calculation is continued from the step (three) again.
Sixthly, outputting the optimal solution of the installation angle deviation after the iteration condition in the step (five) is met
Figure BDA00034665640000001110
And (seventhly) calculating more accurate coordinates of the calibration beacon based on the optimal solution of the installation angle deviation.
Coordinate position of calibration beacon calculated based on direction cosine matrix of installation angle deviation
Figure BDA0003466564000000118
Computing conditional covariance matrices for calibration beacons
Figure BDA0003466564000000119
Thereby obtaining the covariance matrix of the seabed calibration beacon coordinates and reflecting the precision of the coordinates. The calibration precision obtained by the method is consistent with the APOS software precision of foreign Corsberg company through actual measurement experiment verification.
The method for calibrating the ultra-short baseline installation angle deviation by combining adjustment based on the difference technology is described in detail above. The principles and embodiments of the present invention are explained herein using specific examples, which are presented only to assist in understanding the method and its core concepts. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention. The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (8)

1. A combined adjustment calibration method for ultra-short baseline installation angle deviation based on a difference technology is characterized by comprising the following steps:
s1, laying a seabed ultra-short baseline calibration beacon, sailing a measuring ship provided with an ultra-short baseline transducer along a calibration track, and synchronously acquiring and recording differential satellite positioning data, ship course attitude data and acoustic relative positioning data;
s2, constructing a Gaussian Markov model of the combined calibration model by using the calibration data set;
s3, solving a floating point solution of a direction rotation matrix of the installation angle deviation based on the combined adjustment model;
s4, constructing an inter-epoch difference equation based on a joint adjustment model, and solving a direction cosine matrix floating point solution of the angle installation deviation;
s5, carrying out differential floating point solution on non-orthogonal directional cosine matrix
Figure FDA0003466563990000011
Carrying out orthogonalization;
s6, based on a Levenberg-Marquardt iteration method, iteratively calculating an optimal solution of the deviation of the installation angle by using a direction cosine matrix covariance matrix, an angle deviation Euler angle, a floating point solution and a fixed solution;
and S7, calculating more accurate coordinates of the calibration beacon based on the optimal solution of the installation angle deviation obtained in the step S6, and obtaining a conditional covariance matrix of the calibration beacon.
2. The ultrashort baseline installation angle deviation joint adjustment calibration method based on the difference technology as claimed in claim 1, wherein the step S2 specifically includes the following calculation methods:
taking the ZYX coordinate system as an example, let three angular deviation components between the hull coordinate system and the USBL coordinate system be: phi theta psi]Wherein phi is the course angle deviation, theta is the longitudinal rocking angle deviation, psi is the transverse rocking angle deviation, and a direction cosine matrix is set
Figure FDA0003466563990000012
Comprises the following steps:
Figure FDA0003466563990000013
wherein s isα＝sin(α)，cα＝cos(α)；
The position of the GNSS at the time k in a navigation coordinate system is set as
Figure FDA0003466563990000014
The USBL has the coordinates in the navigation coordinate system of
Figure FDA0003466563990000015
The fixed mounting distance deviation between the GNSS and the USBL is Δ X ═ Δ X Δ y Δ z]T，
Figure FDA0003466563990000016
The acoustic relative position of the USBL with respect to the seafloor calibration beacon, that is, the acoustic relative positioning data collected in step S1, can be obtained as follows:
Figure FDA0003466563990000021
wherein
Figure FDA0003466563990000022
B represents a hull coordinate system and n represents a navigation coordinate system for the attitude rotation matrix acquired in the step S1;
setting the USBL to collect m pairs of calibration data, and constructing the following Gaussian Markov model based on all observation data:
Figure FDA0003466563990000023
wherein: e (-) represents a mathematical expectation; y is 3 xm observation value array, Y ═ Y1 y2 … ym]，
Figure FDA0003466563990000024
pBRepresenting coordinates of the seafloor calibration beacon in a navigation coordinate system; a is a coefficient array of 3m multiplied by 3,
Figure FDA0003466563990000025
PUis a 3 × m matrix, and
Figure FDA0003466563990000026
d (-) represents the mathematical variance; qYA covariance matrix of 3m × 3 m; vec (-) denotes the stretch vector of the matrix.
3. The ultra-short baseline installation angle deviation joint adjustment calibration method based on the difference technique as claimed in claim 1, wherein the step S3 specifically includes the following calculation methods:
converting the parameter estimation problem of the Gaussian Markov model obtained in the step S2 into:
Figure FDA0003466563990000027
wherein the content of the first and second substances,
Figure FDA0003466563990000028
SO (3) is a direction rotation matrix,
Figure FDA0003466563990000029
and simultaneously calculating the position of the calibration beacon and the floating solution N of the direction cosine matrix:
Figure FDA00034665639900000210
wherein, I3The unit matrix is a main diagonal element 1, and the rest are 0;
Figure FDA00034665639900000211
a kronecker product representing the matrix;
covariance matrix for calculating floating point solution N
Figure FDA00034665639900000212
Wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00034665639900000213
a location covariance matrix representing the calibration beacon,
Figure FDA00034665639900000214
a cross-covariance matrix representing the calibration beacon and the direction cosine matrix,
Figure FDA0003466563990000031
a covariance matrix representing a directional cosine matrix.
4. The ultra-short baseline installation angle deviation joint adjustment calibration method based on the difference technique as claimed in claim 1, wherein the step S4 specifically includes the following calculation methods:
and (3) subtracting the observation equations at the k and j moments to obtain:
Figure FDA0003466563990000032
at this time, m/2 single difference observation equations are constructed to obtain the following Gaussian Markov model:
Figure FDA0003466563990000033
D(vec(ΔY))＝QΔY
wherein, the delta Y is an observation value array of 3 Xm/2; and Δ Y ═ Δ Y1,m/2+1 Δy2,m/2+2 … Δym/2,m](ii) a Delta A is a parameter matrix of 3m/2 multiplied by 3,
Figure FDA0003466563990000034
ΔPUis a matrix of 3 Xm/2, and
Figure FDA0003466563990000035
QΔYa covariance matrix of 3m/2 × 3 m/2;
converting the parameter estimation problem of the Gaussian Markov model into:
Figure FDA0003466563990000036
and resolving a differential floating point solution delta N of the position and direction cosine matrix of the calibration beacon:
Figure FDA0003466563990000037
wherein, Δ QYIs a covariance matrix;
calculating a covariance matrix of Δ N
Figure FDA0003466563990000038
5. The ultra-short baseline installation angle deviation joint adjustment calibration method based on the difference technique as claimed in claim 1, wherein the step S5 specifically includes the following calculation methods:
orthogonal matrix for calculating direction cosine matrix differential floating point solution
Figure FDA0003466563990000039
Figure FDA0003466563990000041
Computing orthogonal matrices
Figure FDA0003466563990000042
Corresponding Euler angle
Figure FDA0003466563990000043
6. The ultra-short baseline installation angle deviation joint adjustment calibration method based on the difference technique as claimed in claim 1, wherein the step S6 specifically includes the following calculation methods:
jacobian matrix for calculating direction cosine matrix
Figure FDA0003466563990000044
Figure FDA0003466563990000045
Wherein s isαI＝sin(αI)，cαI＝cos(αI)；ΘIFor angular deviation of mounting, thetaI＝[φI θI ψI]；
Calculating an observed value vector
Figure FDA0003466563990000046
Figure FDA0003466563990000047
Calculating the installation angle deviation increment delta thetaI
Figure FDA0003466563990000048
Wherein, λ is a known damping matrix, and is self-adaptively adjusted in an iterative process;
and iteratively calculating the angle installation deviation, and outputting an optimal solution of the angle installation deviation.
7. The ultrashort baseline installation angle deviation joint adjustment calibration method based on the difference technology as claimed in claim 1, wherein in step S6, the iterative calculation of the angle installation deviation specifically includes the following iterative procedures:
s6.1, selecting iteration termination parameter mu1And mu2Damping factor λ and damping scale factor η
S6.2. according to input
Figure FDA0003466563990000051
Calculated by equation (12)
Figure FDA0003466563990000052
Calculation of theta by equation (13)I。
S6.3, calculating the Jacobian matrix by the formula (14)
Figure FDA0003466563990000053
Calculation of an observed value vector by equation (15)
Figure FDA0003466563990000054
S6.4, calculating the mounting angle deviation increment delta theta according to the formula (16)I。
S6.5, carrying out iteration judgment:
if it is not
Figure FDA0003466563990000055
Then λk+1＝λkEta, and the calculation is continued from the step S6.3 again;
otherwise, if
Figure FDA0003466563990000056
And | | | δ ΘI||2≤μ1At this point, the iteration is stopped;
otherwise, if
Figure FDA0003466563990000057
And | | | δ ΘI||2≥μ1Then λk+1＝λkEta, and the calculation is continued from the step S6.3 again;
s6.6, outputting the optimal solution of the installation angle deviation after the iteration condition in the step S6.5 is met
Figure FDA0003466563990000058
。
8. The ultra-short baseline installation angle deviation joint adjustment calibration method based on difference technology as claimed in claim 1, wherein in step S7, the coordinate position of the calibration beacon is calculated based on the direction cosine matrix of the installation angle deviation
Figure FDA0003466563990000059
Computing conditional covariance matrices for calibration beacons
Figure FDA00034665639900000510
Therefore, a conditional covariance matrix of the seabed calibration beacon coordinate is obtained, and the precision of the seabed coordinate is reflected.
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