CN107255810B - Course error compensation method based on single-beacon ranging and positioning double-precision weighted fusion - Google Patents
Course error compensation method based on single-beacon ranging and positioning double-precision weighted fusion Download PDFInfo
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- CN107255810B CN107255810B CN201710605767.0A CN201710605767A CN107255810B CN 107255810 B CN107255810 B CN 107255810B CN 201710605767 A CN201710605767 A CN 201710605767A CN 107255810 B CN107255810 B CN 107255810B
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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
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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
- G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
- G01S15/02—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems using reflection of acoustic waves
- G01S15/06—Systems determining the position data of a target
- G01S15/08—Systems for measuring distance only
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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
- G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
- G01S15/02—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems using reflection of acoustic waves
- G01S15/50—Systems of measurement, based on relative movement of the target
Abstract
The invention discloses a course error compensation method based on single-beacon ranging and positioning double-precision weighting fusion, and belongs to the technical field of underwater acoustic positioning. The method comprises the following steps: respectively obtaining single beacon ranging and positioning results of the 2 beacons on the underwater target in the public action area of the 2 beacons; according to the influence of the target attitude error on the target movement speed, calculating the influence of the target course angle error on the single-beacon ranging positioning result, and determining a weight coefficient in the underwater target acoustic double-precision weighting fusion; and according to the respective single beacon ranging positioning results of the 2 beacons, calculating by using the selected weight coefficient to obtain a positioning result after double-precision weighting fusion. According to the method, the problem of target course angle influence in single-beacon ranging and positioning is solved through a double-precision weighting fusion mode, and the underwater target single-beacon ranging and positioning precision is improved.
Description
Technical Field
The invention belongs to the technical field of underwater acoustic positioning, and particularly relates to a heading error compensation method based on single-beacon ranging positioning double-precision weighting fusion.
Background
At present, technical means (a GPS system, a Galileo system, a Beidou system and the like) mainly based on satellite technology are generally adopted for positioning the aquatic target, and inertia and other positioning technologies are assisted. When the target is underwater, the application of satellite positioning is limited due to the strong absorption of radio waves by the water medium. In this case, the underwater acoustic positioning technology using acoustic waves as information carriers is the main choice, and not only can complete the positioning and navigation of the target, but also can be used as an effective auxiliary calibration means for the inertial positioning and navigation technology.
The underwater acoustic positioning technology is firstly applied to military affairs, and then is gradually applied to various commercial and civil engineering due to the requirements of ocean development, exploration and resource exploitation. It can provide important positioning, navigation and communication support for submarine exploration equipment such as ROV (remote Operated vehicle) and AUV (autonomous Underwater vehicle). By additionally arranging and laying acoustic positioning equipment on the water surface working ship, the underwater mobile platform and the operation sea area, the real-time monitoring of the underwater target position of the water surface and the information interaction of the water surface and the underwater platform can be realized, and the method is a necessary means for engineering such as marine scientific investigation, marine resource exploration, marine resource development, deep sea space station construction and the like.
The positioning method based on single-beacon ranging needs to utilize the geographic position and the target movement speed of a single actually laid beacon. The geographic position of the beacon can be obtained by calibrating the water surface test ship in advance, and belongs to a geodetic coordinate system. The target movement speed is obtained by measuring through an accelerometer or a Doppler velocimeter and is observed quantity under a carrier coordinate system. The positioning and navigation of the underwater target usually adopts a geodetic coordinate system, so the moving speed under a carrier coordinate system needs to be converted into the moving speed under the geodetic coordinate system through a coordinate rotation matrix. The coordinate rotation matrix is composed of target attitude angles, errors of the attitude angles can be transmitted to the positions of the virtual beacons, and then positioning results are influenced, and the target course angle is the most influenced coordinate rotation matrix. In order to solve the problems, the invention provides a heading error compensation method based on single-beacon ranging and positioning double-precision weighting fusion.
Disclosure of Invention
The invention aims to provide a heading error compensation method based on single-beacon ranging and positioning double-precision weighting fusion, which overcomes the influence of a target heading angle error on a coordinate rotation matrix and improves the positioning precision of a single-beacon ranging and positioning system on an underwater target.
The purpose of the invention is realized by the following technical scheme:
the course error compensation method based on single-beacon ranging and positioning double-precision weighted fusion comprises the following steps:
(1) and respectively obtaining the single beacon ranging and positioning results of the 2 beacons on the underwater target in the public action area of the 2 beacons.
(1.1) when the underwater vehicle is located at XbnDuring the process, n virtual beacons are constructed based on the real beacon AT by using the ranging information and the carrier motion parameters of the 1 st to n-1 th ranging periods;
(1.2) obtaining the Beacon Xt1And single beacon ranging positioning result X of underwater target1:
For beacon Xt1Virtual beacon VT1i=(xt1i,yt1i,zt1i)TWith real beacon Xt1Satisfies the following relationship:
using virtual beacons VT1The ranging equation corresponding to the ith ranging period can be written as:
||Xb1n-VT1i||=r1i
adopting Gauss-Newton method to obtain VT based on virtual beacon1The obtained result of single calibration is X1。
(1.3) obtaining Xt2And single beacon ranging positioning result X of underwater target2:
For beacon Xt2Virtual beacon VT2i=(xt2i,yt2i,zt2i)TWith real beacon Xt2Satisfies the following relationship:
using virtual beacons VT2The ranging equation corresponding to the ith ranging period can be written as:
||Xb1n-VT2i||=r2i
by Gauss-Newton method, obtaining a product based onVirtual beacon VT2The obtained result of single calibration is X2。
(2) And according to the influence of the target attitude error on the target movement speed, calculating the influence of the target course angle error on the single-beacon ranging positioning result, and determining a weight coefficient during the underwater target acoustic double-precision weighted fusion.
(2.1) the positioning result after double-precision weighted fusion of the double-confidence positioning result can be represented by the following formula:
X12=ω1X1+ω2X2
wherein, X1As a single beacon Xt1Positioning result of (1), X2As a single beacon Xt2Positioning result of (1), X12For the positioning result after weighted fusion of the positioning results of the two beacons, omega1And ω2Weight coefficients that are weighted fusions;
According to the theory of minimum mean square error, the weight coefficient omega1And ω2When selecting, the final positioning result X of the target is required to be obtained12And the true position X of the targetbMinimum mean square error of (d):
wherein the content of the first and second substances,the mean square error of the positioning result after the weighted fusion of the positioning results of the double-signal calibration is obtained;
since the single positioning results of the two beacons to the target are independent and the weight coefficients have to satisfy the unbiased requirement, the mean square error is obtained
(2.3) the cost function constructed in the Lagrange multiplier method is as follows:
(2.4) determining a weight coefficient omega for weighted fusion1And ω2:
When the following formula is satisfied, the positioning result precision after the weighted fusion of the double-beacon positioning result is the highest:
weight coefficient omega of weighted fusion1And ω2Can be described as:
(3) and according to the respective single beacon ranging positioning results of the 2 beacons, calculating by using the selected weight coefficient to obtain a positioning result after double-precision weighting fusion.
The positioning result after double-precision weighted fusion of the double-beacon positioning result can be represented by the following formula:
X12=ω1X1+ω2X2
in particular:
the method for respectively obtaining the single-beacon ranging and positioning results of the 2 beacons to the underwater target in the public action area of the 2 beacons comprises the following steps: when the target works in the public action area of 2 beacons, two beacons X can be respectively obtained according to the single-beacon ranging positioning method based on the virtual ranging beacont1And Xt2Single beacon ranging positioning result X for underwater target1And X2The two positioning results are independent.
The method for determining the weight coefficient during the underwater target acoustic double-precision weighted fusion comprises the following steps of calculating the influence of the target course angle error on the single-beacon ranging positioning result according to the influence of the target attitude error on the target movement speed, wherein the weight coefficient is obtained by the following steps: the coordinate rotation matrix is composed of target attitude angles, errors of the attitude angles can be transmitted to the positions of the virtual beacons, and then positioning results are influenced, and the target course angle is the most influenced coordinate rotation matrix. When course errors exist, horizontal positioning errors are symmetrically distributed, the positioning errors at the beacon are the smallest, the beacon is used as the center to radiate outwards, and the positioning errors of areas which are farther away from the beacon are larger.
The method for obtaining the positioning result after double-precision weighting fusion by utilizing the selected weight coefficient calculation according to the single-beacon ranging positioning result of each of the 2 beacons comprises the following steps: and (3) calculating the independent 2 single-beacon ranging positioning results based on a double-precision weighting fusion principle by combining weight coefficients determined by the positioning error spatial distribution characteristics caused by the target course error to obtain a positioning result after course error compensation.
The invention has the beneficial effects that:
in the public action area of 2 beacons, respectively obtaining single beacon ranging and positioning results of two beacons on an underwater target according to a single beacon ranging and positioning method based on the virtual ranging beacon; determining a weight coefficient during the double-precision weighted fusion of underwater target acoustics according to the influence of the course angle error on the horizontal positioning result; and calculating to obtain a positioning result after course error compensation based on a double-precision weighting fusion principle. The method solves the influence of the target course error on the coordinate rotation matrix and the single-beacon ranging and positioning result, and improves the positioning accuracy of the single-beacon ranging and positioning system.
Drawings
FIG. 1 is a positioning result of a beacon located on an opposite side of a target track;
fig. 2 shows the positioning error of the beacon located on the opposite side of the target track.
Detailed Description
The following further describes embodiments of the present invention with reference to the accompanying drawings:
the course error compensation method based on single-beacon ranging and positioning double-precision weighting fusion is characterized by comprising the following steps of:
(1) respectively obtaining single beacon ranging and positioning results of the 2 beacons on the underwater target in the public action area of the 2 beacons;
(2) according to the influence of the target attitude error on the target movement speed, calculating the influence of the target course angle error on the single-beacon ranging positioning result, and determining a weight coefficient in the underwater target acoustic double-precision weighting fusion;
(3) and according to the respective single beacon ranging positioning results of the 2 beacons, calculating by using the selected weight coefficient to obtain a positioning result after double-precision weighting fusion.
The specific implementation method of the step (1) comprises the following steps:
(1.1) when the underwater vehicle is located at XbnDuring the process, n virtual beacons are constructed based on the real beacon AT by using the ranging information and the carrier motion parameters of the 1 st to n-1 th ranging periods;
(1.2) obtaining the Beacon Xt1And single beacon ranging positioning result X of underwater target1:
For beacon Xt1Virtual beacon VT1i=(xt1i,yt1i,zt1i)TWith real beacon Xt1Satisfies the following relationship:
using virtual beacons VT1The ranging equation corresponding to the ith ranging period can be written as:
||Xb1n-VT1i||=r1i
adopting Gauss-Newton method to obtain VT based on virtual beacon1The obtained result of single calibration is X1。
(1.3) obtaining Xt2And single beacon ranging positioning result X of underwater target2:
For beacon Xt2Virtual beacon VT2i=(xt2i,yt2i,zt2i)TWith real beacon Xt2Satisfies the following relationship:
using virtual beacons VT2The ranging equation corresponding to the ith ranging period can be written as:
||Xb1n-VT2i||=r2i
adopting Gauss-Newton method to obtain VT based on virtual beacon2The obtained result of single calibration is X2。
The specific implementation method of the step (2) comprises the following steps:
(2.1) the positioning result after double precision weighted fusion of the double confidence positioning result can be represented by the following formula:
X12=ω1X1+ω2X2(1)
wherein, X1As a single beacon Xt1Positioning result of (1), X2As a single beacon Xt2Positioning result of (1), X12For the positioning result after weighted fusion of the positioning results of the two beacons, omega1And ω2Are weighted fused weight coefficients.
(2.2) weight coefficient omega of weighted fusion1And ω2Final positioning result X for target12The influence is great, and according to the theory of minimum mean square error, the weight coefficient omega1And ω2When selecting, the final positioning result X of the target is required to be obtained12And the true position X of the targetbMinimum mean square error of (d):
wherein the content of the first and second substances,and the mean square error of the positioning result after the weighted fusion of the positioning results of the two beacons is obtained.
Since the single positioning results of the two beacons on the target are independent and the weight coefficients have to satisfy the unbiased requirement, the first progress is obtainedSquare error
(2.3) weight coefficient omega of weighted fusion1And ω2Selecting the optimal positioning result which can be described as the optimization problem under the constraint of the positioning result after the weighted fusion of the positioning results of the two beacons, wherein the cost function constructed when the Lagrange multiplier method is used for solving is as follows:
(2.4) weighting the weight coefficient omega of the fusion1And ω2And when the following formula is met, the positioning result precision after the weighted fusion of the double-beacon positioning result is highest.
According to the result of the target attitude error influence analysis, when a fixed course error exists, the horizontal positioning errors are symmetrically distributed, the positioning error at the beacon is the minimum, the beacon is used as the center to radiate outwards, and the positioning error of an area which is farther away from the beacon is larger. Thus, the weight coefficient ω of the weighted fusion1And ω2Can be described as:
the specific implementation method of the step (3) comprises the following steps:
the positioning result after double-precision weighted fusion of the double-beacon positioning result can be represented by the following formula:
X12=ω1X1+ω2X2。
example (b):
the course error compensation method based on the single-beacon ranging and positioning double-precision weighting fusion is subjected to simulation analysis.
The two acoustic beacons placed on the sea floor are at positions (-1500, -1500,3600) m and (1500,1500,3600) m, respectively, with the beacons being located on opposite sides of the target track. The underwater target makes forward linear motion at a constant depth 3700m and a uniform speed of 1m/s, and sails at a course of 90 degrees for 3000 m. The ranging period is 20s, and the number of virtual beacons is 15. The method comprises the steps of adding a random error with standard deviation of 0.15m to distance measurement, adding a random error with standard deviation of 3% o.v. +0.002m/s to a target forward speed, adding a random error with standard deviation of 0.002m/s to a target right speed, adding a random error with standard deviation of 0.1 degrees to a target course angle, and adding a fixed error of +1 degrees. When the initial target position is (-1500,0) m, the single-beacon ranging positioning results and the positioning results after double-precision weighting fusion corresponding to different beacons are shown in fig. 1. It can be seen from the figure that the degree of deviation of the single-beacon positioning result from the real track increases with the distance from the beacon, and the directions of deviation of the real track from the single-beacon positioning results at the two ends of the minimum distance of the beacon are opposite. The positioning result after weighted fusion is obviously better than the single beacon ranging positioning result of any one beacon. The single beacon ranging positioning error and the double-precision weighted positioning error corresponding to different beacons are shown in fig. 2. As can be seen from the figure, the weighted fusion positioning error is significantly smaller than the single-beacon ranging positioning error of any one beacon, the positioning error decreases with the decrease of the distance difference between the target and the two beacons, and the positioning error decreases from 20m to 0 m.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (3)
1. The course error compensation method based on single-beacon ranging and positioning double-precision weighting fusion is characterized by comprising the following steps of:
(1) respectively obtaining single beacon ranging and positioning results of the 2 beacons on the underwater target in the public action area of the 2 beacons;
(2) according to the influence of the target attitude error on the target movement speed, calculating the influence of the target course angle error on the single-beacon ranging positioning result, and determining a weight coefficient in the underwater target acoustic double-precision weighting fusion;
(3) according to the respective single beacon ranging positioning results of the 2 beacons, the positioning result after double-precision weighting fusion is obtained by utilizing the selected weight coefficient;
the specific implementation method of the step (1) comprises the following steps:
(1.1) when the underwater vehicle is located at XbnDuring the process, n virtual beacons are constructed based on the real beacon AT by using the ranging information and the carrier motion parameters of the 1 st to n-1 th ranging periods;
(1.2) obtaining the Beacon Xt1And single beacon ranging positioning result X of underwater target1:
For beacon Xt1Virtual beacon VT1i=(xt1i,yt1i,zt1i)TWith real beacon Xt1Satisfies the following relationship:
using virtual beacons VT1The ranging equation corresponding to the ith ranging period is written as:
||Xb1n-VT1i||=r1i
adopting Gauss-Newton method to obtain VT based on virtual beacon1The obtained result of single calibration is X1;
(1.3) obtaining Xt2And single beacon ranging positioning result X of underwater target2:
For beacon Xt2Virtual beacon VT2i=(xt2i,yt2i,zt2i)TWith real beacon Xt2Satisfies the following relationship:
using virtual beacons VT2The ranging equation corresponding to the ith ranging period is written as:
||Xb1n-VT2i||=r2i
adopting Gauss-Newton method to obtain VT based on virtual beacon2The obtained result of single calibration is X2;
Single beacon ranging and positioning result X of underwater target1And X2Is independent;
the specific implementation method of the step (2) comprises the following steps:
(2.1) the positioning result after double-precision weighted fusion of the double-confidence positioning result can be represented by the following formula:
X12=ω1X1+ω2X2
wherein, X1As a single beacon Xt1Positioning result of (1), X2As a single beacon Xt2Positioning result of (1), X12For the positioning result after weighted fusion of the positioning results of the two beacons, omega1And ω2Weight coefficients that are weighted fusions;
According to the theory of minimum mean square error, the weight coefficient omega1And ω2When selecting, the final positioning result X of the target is required to be obtained12And the true position X of the targetbMinimum mean square error of (d):
wherein the content of the first and second substances,the mean square error of the positioning result after the weighted fusion of the positioning results of the double-signal calibration is obtained;
since the single positioning results of the two beacons to the target are independent and the weight coefficients have to satisfy the unbiased requirement, the mean square error is obtained
(2.3) the cost function constructed in the Lagrange multiplier method is as follows:
(2.4) determining a weight coefficient omega for weighted fusion1And ω2:
When the following formula is satisfied, the positioning result precision after the weighted fusion of the double-beacon positioning result is the highest:
weight coefficient omega of weighted fusion1And ω2The description is as follows:
2. the single-beacon ranging and positioning double-precision weighted fusion-based course error compensation method as claimed in claim 1, wherein when a course error exists, the horizontal positioning error is distributed symmetrically, the positioning error at the beacon is the smallest, the positioning error is radiated outwards by taking the beacon as a center, and the positioning error of the area farther away from the beacon is larger.
3. The heading error compensation method based on single-beacon ranging and positioning double-precision weighted fusion as claimed in claim 1, wherein the implementation method of the step (3) comprises:
the positioning result after double-precision weighted fusion of the double-beacon positioning result can be represented by the following formula:
X12=ω1X1+ω2X2。
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