CN110441760B - Wide-range seabed topographic map expansion composition method based on prior topographic map - Google Patents

Wide-range seabed topographic map expansion composition method based on prior topographic map Download PDF

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CN110441760B
CN110441760B CN201910870773.8A CN201910870773A CN110441760B CN 110441760 B CN110441760 B CN 110441760B CN 201910870773 A CN201910870773 A CN 201910870773A CN 110441760 B CN110441760 B CN 110441760B
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CN110441760A (en
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王汝鹏
徐鹏飞
骆佳成
程红霞
张驰
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Hohai University HHU
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
    • G01S7/539—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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Abstract

The invention discloses a large-range seabed topographic map expanding composition method based on a priori topographic map, which comprises the following processes: s1, taking a determined alignment point in a priori topographic map as a starting point, surveying and mapping an unknown region outside the priori topographic map along a retracing path to obtain sonar surveying and mapping data, and returning to a reentry point in the priori topographic map to finish the surveying and mapping; s2, repeating the step S1 until the detection is finished; s3, constructing a global constraint mathematical model according to the data obtained by mapping; and S4, solving the optimal solution of the mathematical model to obtain the position of each flight measuring point on the turn-back path. The invention uses the prior topographic map to position the carrier and the measured topographic map, and carries out large-scale composition by establishing the constraint relation of the sub-map, thereby obtaining a global consistency map with higher precision.

Description

Wide-range seabed topographic map expanding composition method based on prior topographic map
Technical Field
The invention belongs to the technical field of underwater topographic mapping, and particularly relates to a large-range seabed topographic map expansion composition method based on a priori topographic map.
Background
Due to the limitation of underwater navigation and positioning technology, the acquisition process of the underwater topographic map which is relatively accurate in a large range is relatively difficult at present. At present, precise terrain in a small range is mainly mapped through an AUV (autonomous underwater vehicle), but the coordinate origin of each small terrain map is difficult to maintain consistency due to the limitation of underwater positioning precision.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a large-range seabed topographic map expansion composition method based on a priori topographic map.
In order to solve the problems in the prior art, the invention discloses a large-range seabed topographic map expansion composition method based on a priori topographic map, which comprises the following processes:
s1, taking a determined alignment point in a priori topographic map as a starting point, surveying and mapping an unknown region outside the priori topographic map along a retracing path to obtain sonar surveying and mapping data, and returning to a reentry point in the priori topographic map to finish the surveying and mapping; wherein, the surveying and mapping process meets the following requirements:
at least two mapping sub-maps from different groups are overlapped in two groups of mapping sub-maps respectively acquired by a starting section and a turning section of the same turning path; at least two mapping sub-maps from different groups are overlapped in two groups of mapping sub-maps respectively acquired by a return section of the mapping reentry path and a starting section of the next mapping reentry path;
s2, repeating the step S1 until the detection is finished;
s3, constructing a global constraint mathematical model according to the data obtained by mapping;
and S4, solving the optimal solution of the mathematical model to obtain the position of each navigation point on the turn-back path.
Further, the air conditioner is characterized in that,
in step S1, the method for determining the alignment point includes the following steps:
calculating the mean value and the variance of the particle set sequence corresponding to any position point in the terrain matching navigation process, wherein the particle set sequence comprises particle position coordinates and likelihood values,
calculating a covariance matrix according to the variance of the particle set sequence;
calculating the Gaussian distribution probability value of each particle according to the covariance matrix;
and judging whether the navigation system of the current position point meets a convergence condition or not according to the likelihood value, the Gaussian distribution probability value and a preset threshold of the particle sequence, if so, determining that the position is the position of the alignment point, otherwise, replanning terrain matching navigation until the alignment point is found.
Further, the air conditioner is characterized in that,
the expression of the particle set sequence corresponding to any position point is as follows: (x) i ,y i ,l i ) N, where x is x =1,2,3 i And y i Is the position coordinate of the particle at time i, l i The likelihood value of the particle at the time point i is shown, and n is the total number of the particles in the particle set;
the mean value calculation formula of the particle set sequence is as follows:
Figure GDA0004053421780000021
the variance calculation formula of the particle set sequence is as follows:
Figure GDA0004053421780000022
the expression of the covariance matrix is:
Figure GDA0004053421780000023
the calculation formula of the Gaussian distribution probability value is as follows:
Figure GDA0004053421780000024
wherein the content of the first and second substances,
Figure GDA0004053421780000025
the convergence condition is as follows:
if delta is less than epsilon, the navigation system is converged;
wherein the content of the first and second substances,
Figure GDA0004053421780000026
epsilon is a preset threshold value of the navigation system.
Further, the air conditioner is provided with a fan,
in step S1, the determination of the re-entry point includes the following steps:
calculating the mean value and the variance of the particle set sequence corresponding to any position point in the terrain matching navigation returning process, wherein the particle set sequence comprises particle position coordinates and likelihood values,
calculating error intervals of an error ellipse and a rectangle according to the variance of the particle set sequence;
and if the error interval completely enters the prior topographic map area, the position is a re-entry point.
Further, the air conditioner is provided with a fan,
the expression of the particle set sequence corresponding to any position point in the process of returning according to terrain matching navigation is as follows: (x) i ',y i ',l i '), i =1,2,3 i ' and y i ' is the position coordinate of the moment of the particle i,/ i ' is the likelihood value of the particle at the moment i, and n is the total number of particles in the particle set;
the calculation formula of the mean value is as follows:
Figure GDA0004053421780000031
the calculation formula of the variance is as follows:
Figure GDA0004053421780000032
the calculation formula of the error interval of the error ellipse and the rectangle is as follows:
Figure GDA0004053421780000033
wherein theta represents the angle between the major axis of the ellipse and the horizontal axis of the coordinate, and lambda 1 And λ 2 Respectively representing the lengths of the major and minor axes of the ellipse, whereby the interval defined by the ellipse is re-entered by the navigation systemAnd (4) positioning error interval of the range.
Further, the air conditioner is provided with a fan,
the process of constructing the globally constrained mathematical model from the mapped data is as follows:
establishing association constraint according to mapping sub-maps with overlapping areas respectively obtained by adjacent departure sections and return sections,
a positioning error is calculated based on the association constraint,
and establishing a global constraint mathematical model according to the positioning error, the system error and the calculation error.
Further, the air conditioner is provided with a fan,
the expression of the association constraint is:
Figure GDA0004053421780000041
wherein C represents a normalization constant, Z a And Z b Representing sequence heights of overlapping areas of the mappers, Λ representing measurement errors of the terrain;
the calculation formula of the positioning error is as follows:
Figure GDA0004053421780000042
the calculation formula of the calculation error is as follows:
Figure GDA0004053421780000043
wherein, F i,i+1 A state transition matrix from the moment i to the moment i +1 of the navigation system is used as a reference; q i,i+1 The observation error of the navigation system from the moment i to the moment i +1 is used as a reference; p i A reference navigation system error representing time i;
the expression of the mathematical model of the global constraint is as follows:
Figure GDA0004053421780000044
wherein the content of the first and second substances,
Figure GDA0004053421780000045
is a systematic error, is asserted>
Figure GDA0004053421780000046
Indicating the positioning error between the map sub-map k and the map sub-map l.
Further, the air conditioner is provided with a fan,
in step S1, the access point is located at the boundary of the prior topographic map.
Further, the air conditioner is provided with a fan,
in step S1, the foldback path satisfies the following requirements:
Figure GDA0004053421780000047
in which L is the width of the measuring strip of the detector, S 1 The vertical distance between the starting section and the returning section of the reentry path in the mapping is taken as the vertical distance; s 2 Is the vertical distance between the departure section of the reentrant path in the next survey and the return section of the reentrant path in the current survey.
The invention has the following beneficial effects:
1. the invention can incrementally construct a large-range submarine topographic map based on the existing small-range prior topographic map, and particularly can remarkably improve the surveying and mapping precision and speed aiming at polar regions and deep sea environments.
2. The map constructed by the invention meets the global consistency requirement, and the coordinate system of each sub-map is aligned with the coordinate system of the prior topographic map, so that the surveying and mapping precision is ensured.
3. The method can realize autonomous measurement and map construction by taking the AUV as a carrier, and has wide application foundation and popularization value.
Drawings
FIG. 1 is a schematic diagram of the mapping process of the present invention;
FIG. 2 is a schematic diagram of a primary alignment point determination according to the present invention;
FIG. 3 is a schematic diagram of a single mapping according to the present invention;
FIG. 4 is a schematic diagram illustrating the principle of the present invention for repeated alignment point determination;
FIG. 5 is a schematic diagram of the principles of the present invention for repeated mapping;
FIG. 6 is a schematic diagram of the association constraint construction of the present invention;
FIG. 7 is a schematic diagram of the construction of a fully constrained model according to the present invention;
FIG. 8 is a flow chart of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
As shown in fig. 1 to 8, a wide-range submarine topographic map extension composition method based on a priori topographic map includes the following processes:
s1, taking a determined alignment point 6 in a priori topographic map 1 as a starting point, surveying and mapping an unknown region 8 outside the priori topographic map along a retracing path 7 to obtain sonar surveying and mapping data, and then returning to a reentry point 10 in the priori topographic map 1 to finish the surveying and mapping. Wherein, the surveying and mapping process meets the following requirements:
at least two mapping sub-maps from different groups are overlapped in two groups of mapping sub-maps respectively acquired by a starting section and a turning section of the same turning path; at least two mapping sub-maps from different groups are overlapped in two groups of mapping sub-maps respectively acquired by a return section of the turn-back path of the current mapping and a start section of the turn-back path of the next mapping. The greater the number of survey sub-maps that overlap occurs, the higher the survey accuracy.
In the process, in order to improve the accuracy of each survey, an alignment point 6 needs to be determined in the prior topographic map 1 before each survey, and then the extended survey is carried out by taking the alignment point 6 as a starting point.
As shown in fig. 2, before each survey, a starting point 2 and an end point 3 of a navigation path 4 are planned according to a priori terrain map 1, and then filtering navigation is performed by using the terrain matching navigation technology of the AUV to find an alignment point 6.
The determination of the alignment point 6 comprises the following processes:
setting an expression of a particle set sequence corresponding to any position point in the filtering navigation process as follows:
(x i ,y i ,l i ) N, where x is x =1,2,3 i And y i Is the position coordinate of the particle at time i,/ i The likelihood value of the particle at the time point i is shown, and n is the total number of the particles in the particle set;
calculating the mean and variance of the particle set sequence in step S11, wherein the mean expression is:
Figure GDA0004053421780000061
the variance expression is:
Figure GDA0004053421780000062
s13, calculating a covariance matrix according to the variance of the particle set sequence, wherein the expression of the covariance matrix is as follows:
Figure GDA0004053421780000063
s14, calculating the Gaussian distribution probability value of each particle according to the covariance matrix, wherein the expression of the Gaussian distribution probability value is as follows:
Figure GDA0004053421780000064
wherein the content of the first and second substances,
Figure GDA0004053421780000065
and judging whether the current position point navigation system meets a convergence condition or not according to the likelihood value, the Gaussian distribution probability value and a preset threshold of the particle sequence, if so, determining that the position is the position of the alignment point 6, otherwise, re-navigating until the alignment point 6 is found. The convergence conditions are as follows:
if delta is less than epsilon, the matched navigation filtering system is converged;
wherein the content of the first and second substances,
Figure GDA0004053421780000066
ε is a preset threshold value for the navigation system, which is a known quantity.
The closer the alignment point is to the boundary of the a priori topographic map 1, the higher the accuracy of the mapping process, so to ensure that the mapping accuracy is maintained at the highest level, in determining the alignment point 6, it is preferable to determine the point on the boundary of the a priori topographic map 1 as the alignment point, and the AUV can map with the greatest navigation accuracy.
In step S1, the determination of the re-entry point 10 includes the following steps:
setting an expression of a particle set sequence corresponding to any position point in the navigation returning process as follows: (x) i ',y i ',l i '), i =1,2,3 i ' and y i ' is the position coordinate of the moment of the particle i,/ i ' is the likelihood of the particle at time i, and n is the total number of particles in the set of particles.
The calculation formula of the mean value is as follows:
Figure GDA0004053421780000071
the variance is calculated as:
Figure GDA0004053421780000072
the calculation formula of the error interval of the error ellipse and the rectangle is as follows:
Figure GDA0004053421780000073
wherein θ represents the length of the ellipseAngle between axis and axis of the coordinate, λ 1 And λ 2 The lengths of the major axis and the minor axis of the ellipse are respectively expressed, and the interval determined by the ellipse is the positioning error interval of the reentrant process of the navigation system.
The interval determined by the ellipse is a positioning error interval in the reentry process of the navigation system, if the error interval completely enters the area of the prior topographic map 1, the position is the reentry point 10, otherwise, the navigation is planned again until the reentry point 10 is found.
In step S1, in order to ensure that the sub-map obtained by mapping at any segment of the departure segment of the AUV can find the sub-map obtained by mapping at any segment of the return segment of the AUV during the course of surveying along the return path 7, and the sub-map is overlapped with the sub-map to generate the association constraint, the return path 7 should satisfy the following requirements:
Figure GDA0004053421780000081
in which L is the width of the measuring strip of the detector, S 1 Is the vertical distance between the departure section 71 and the return section 72 of the reentry path 7 in this survey; s 2 Is the vertical distance between the departure section 71 of the reentrant path 7 in the next survey and the return section 72 of the reentrant path 7 in the present survey.
In order to take mapping efficiency and correlation matching degree into consideration, L, S 1 、S 2 Satisfies the following conditions:
Figure GDA0004053421780000082
and S2, as shown in the figures 4 and 5, repeating the step S1 until the detection of the unknown region 8 to be detected around the prior topographic map 1 is completed.
S3, as shown in FIG. 6, a global constraint mathematical model is constructed according to the data obtained by mapping, and the process is as follows:
because there is an overlapping area between the surveying and mapping sub-maps respectively obtained by the departure segment 71 and the return segment 72, the association constraint can be constructed according to sub-map matching positioning, and because the association degree between the central points of the two sub-maps k and l is determined by the terrain matching positioning error J, the association constraint needs to be determined first, and the expression is:
Figure GDA0004053421780000083
wherein C represents a normalization constant, Z k And Z l Representing the sequence heights of the overlapping areas of the mappers k and l, and Λ representing the measurement error of the terrain.
And calculating the positioning error according to the association constraint, wherein the calculation formula is as follows:
Figure GDA0004053421780000084
and finally forming the global constraint relation of the air route according to the obtained positioning information and the constraint relation. As shown in fig. 7, the global constraint relationship of the course line is composed of black triangles (i.e., terrain matching navigation fix points and course line control points), and black solid circles, where the terrain matching navigation points need to account for positioning errors. For the convenience of establishing a mathematical model, all constraints are divided into 3 types, which are:
1. the reference navigation positioning of two adjacent control points is respectively counted as
Figure GDA0004053421780000085
And &>
Figure GDA0004053421780000086
Positioning error is counted as>
Figure GDA0004053421780000087
The expression is as follows: />
Figure GDA0004053421780000088
In the formula: f i,i+1 A state transition matrix representing the system; q i,i+1 Indicating the observation error of the system.
2. From matching locations between individual sub-mapsResulting constraint, anchor point meter
Figure GDA0004053421780000089
The positioning error meter is->
Figure GDA00040534217800000810
Where k and l represent the index sequence numbers of the two sub-maps with data association, respectively.
3. Given by the terrain-matched navigation system, the localization points are counted as
Figure GDA00040534217800000811
The positioning error meter is->
Figure GDA00040534217800000812
The constraint relation between the track control points needs to consider the association degree, the higher the association degree is, the thicker the connecting line between the track control points is, and the thinner the connecting line is. And constructing a mathematical model according to the global constraint, wherein the expression is as follows:
Figure GDA0004053421780000091
and S4, solving the minimum value of the mathematical model in the step S3 to obtain the optimal solution of the position of the track control point. The optimal result of the global map can be obtained after the optimal solution set of the control points of the flight path is obtained.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (8)

1. A large-range seabed topographic map expansion composition method based on a priori topographic map is characterized in that: the method comprises the following steps:
s1, taking a determined alignment point in a priori topographic map as a starting point, surveying and mapping an unknown region outside the priori topographic map along a retracing path to acquire sonar surveying and mapping data, and returning to a reentry point in the priori topographic map to finish surveying and mapping; wherein, the surveying and mapping process meets the following requirements:
at least two mapping sub-maps from different groups are overlapped in two groups of mapping sub-maps respectively acquired by a starting section and a turning section of the same turning path; at least two mapping sub-maps from different groups are overlapped in two groups of mapping sub-maps respectively acquired by a return section of the mapping reentry path and a starting section of the next mapping reentry path;
s2, repeating the step S1 until the detection is finished;
s3, constructing a global constraint mathematical model according to the data obtained by mapping, wherein the global constraint mathematical model comprises the following steps: establishing association constraint according to surveying and mapping sub-maps with overlapping areas respectively obtained by the adjacent starting section and the returning section, calculating a positioning error according to the association constraint, and establishing a global constraint mathematical model according to the positioning error, the system error and the calculation error;
and S4, solving the optimal solution of the mathematical model to obtain the position of each navigation point on the turn-back path.
2. The extensive submarine topography map extended composition method based on the prior topography map according to claim 1, characterized in that:
in step S1, the method for determining the alignment point includes the following steps:
calculating the mean value and the variance of the particle set sequence corresponding to any position point in the terrain matching navigation process, wherein the particle set sequence comprises particle position coordinates and likelihood values,
calculating a covariance matrix according to the variance of the particle set sequence;
calculating the Gaussian distribution probability value of each particle according to the covariance matrix;
and judging whether the navigation system of the current position point meets a convergence condition or not according to the likelihood value, the Gaussian distribution probability value and a preset threshold of the particle sequence, if so, determining that the position is the position of the alignment point, otherwise, replanning terrain matching navigation until the alignment point is found.
3. The extensive seafloor topographic map expansion mapping method based on the prior topographic map as claimed in claim 2, wherein the method comprises the following steps:
the expression of the particle set sequence corresponding to any position point is as follows: (x) i ,y i ,l i ) N, where x is x =1,2,3 i And y i Is the position coordinate of the particle at time i,/ i The likelihood value of the particle at the time i, and n is the total number of the particles in the particle set;
the mean value calculation formula of the particle set sequence is as follows:
Figure FDA0004053421770000021
the variance calculation formula of the particle set sequence is as follows:
Figure FDA0004053421770000022
the expression of the covariance matrix is:
Figure FDA0004053421770000023
the calculation formula of the Gaussian distribution probability value is as follows:
Figure FDA0004053421770000024
wherein the content of the first and second substances,
Figure FDA0004053421770000025
the convergence condition is as follows:
if delta is less than epsilon, the navigation system is converged;
wherein the content of the first and second substances,
Figure FDA0004053421770000026
epsilon is a preset threshold value of the navigation system.
4. The extensive submarine topography map extended composition method based on the prior topography map according to claim 3, characterized in that:
in step S1, the determination of the re-entry point includes the following steps:
calculating the mean value and the variance of the particle set sequence corresponding to any position point in the terrain matching navigation returning process, wherein the particle set sequence comprises particle position coordinates and likelihood values,
calculating error intervals of an error ellipse and a rectangle according to the variance of the particle set sequence;
and if the error interval completely enters the prior topographic map area, the position is a re-entry point.
5. The extensive submarine topography map extended composition method based on the prior topography map according to claim 4, characterized in that:
the expression of the particle set sequence corresponding to any position point in the terrain matching navigation returning process is as follows: (x) i ',y i ',l i '), i =1,2,3 i ' and y i ' is the position coordinate of the particle at time i, l i ' is the likelihood value of the particle i moment, and n is the total number of particles in the particle set;
the calculation formula of the mean value is as follows:
Figure FDA0004053421770000031
the calculation formula of the variance is as follows:
Figure FDA0004053421770000032
the calculation formula of the error interval of the error ellipse and the rectangle is as follows:
Figure FDA0004053421770000033
wherein theta represents the angle between the major axis of the ellipse and the horizontal axis of the coordinate, and lambda 1 And λ 2 Respectively representing the lengths of the major axis and the minor axis of the ellipse, and the interval determined by the ellipse is the positioning error interval of the reentry process of the navigation system.
6. The extensive seafloor topographic map expansion mapping method based on the prior topographic map as claimed in claim 5, wherein the method comprises the following steps:
the expression of the association constraint is:
Figure FDA0004053421770000041
wherein C represents a normalization constant, Z a And Z b Representing sequence heights of overlapping areas of the mappers, Λ representing measurement errors of the terrain;
the calculation formula of the positioning error is as follows:
Figure FDA0004053421770000042
the calculation formula of the calculation error is as follows:
Figure FDA0004053421770000043
wherein, F i,i+1 A state transition matrix from the moment i to the moment i +1 of the navigation system is used as a reference; q i,i+1 The observation error of the navigation system from the moment i to the moment i +1 is used as a reference; p i A reference navigation system error representing time i;
the expression of the mathematical model of the global constraint is as follows:
Figure FDA0004053421770000044
wherein the content of the first and second substances,
Figure FDA0004053421770000045
in the form of system errors>
Figure FDA0004053421770000046
Indicating the positioning error between the map sub-map k and the map sub-map l.
7. The extensive submarine topography map extended mapping method based on the prior topography map according to any one of claims 1 to 6, characterized in that:
in step S1, the access point is located at the boundary of the prior topographic map.
8. The extensive submarine topography map extended mapping method based on the prior topography map according to any one of claims 1 to 6, characterized in that:
in step S1, the foldback path satisfies the following requirements:
Figure FDA0004053421770000047
in which L2 is the width of the measuring strip of the detector, S 1 The vertical distance between the starting section and the returning section of the reentry path in the mapping is taken as the vertical distance; s 2 Is the vertical distance between the starting section of the retrace path in the next survey and the returning section of the retrace path in the current survey. />
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