CN112526523B - Improved multi-base sound localization method - Google Patents
Improved multi-base sound localization method Download PDFInfo
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- CN112526523B CN112526523B CN202011194596.5A CN202011194596A CN112526523B CN 112526523 B CN112526523 B CN 112526523B CN 202011194596 A CN202011194596 A CN 202011194596A CN 112526523 B CN112526523 B CN 112526523B
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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
- G01S15/88—Sonar systems specially adapted for specific applications
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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
- G01S15/46—Indirect determination of position data
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- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Physics & Mathematics (AREA)
- Acoustics & Sound (AREA)
- Computer Networks & Wireless Communication (AREA)
- General Physics & Mathematics (AREA)
- Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)
Abstract
The invention discloses an improved multi-base sonar positioning method, belongs to the technical field of sonar detection methods, and solves the technical problem of lower calculation accuracy of the method in the prior art. S101, determining a measurement equation according to each station address in a multi-base sound receiving system, obtaining a linear equation set through mathematical transformation, and obtaining an initial value of a target position through a least square algorithm; s102, carrying out Taylor series expansion on the measurement equation at the initial value of the target position, and determining the accurate value of the target position, the iteration number N and the position residual error delta 1 The method comprises the steps of carrying out a first treatment on the surface of the S103: according to the iteration number N and the position residual error delta 1 The final value of the target position is determined. The method is used for improving the precision of multi-base sound positioning.
Description
Technical Field
The invention belongs to the technical field of sonar detection methods, and relates to an improved multi-base sonar positioning method.
Background
The multi-base sound receiving system has the advantages of large detection range, good concealment, strong anti-interference capability and rich target information, and is always a hotspot direction for research in the field of underwater sound detection. The method has wide application prospect in anti-diving, underwater target detection and ocean monitoring. Multi-base localization algorithms have been studied by many scholars as a key technology for multi-base sound detection systems. Specific positioning algorithms include a linear least squares based multi-base positioning algorithm, a weighted least squares based multi-base positioning algorithm, an overall least squares based positioning algorithm, and the like. The taylor series expansion least square algorithm results in poor positioning results due to poor initial selection.
In view of this, the present invention has been made.
Disclosure of Invention
The invention aims to provide a multi-base sound location method, which solves the technical problem of lower calculation precision of the method in the prior art. The technical scheme of the scheme has a plurality of technical advantages, and the following description is provided:
an improved method of multi-base sound localization is provided, the method comprising:
s101, determining a measurement equation according to each station address in a multi-base sound system, obtaining a linear equation set through mathematical transformation, and obtaining an initial value of a target position through a least square algorithm;
s102, carrying out Taylor series expansion on the measurement equation at the initial value of the target position, and determining the accurate value of the target position, the iteration number N and the position residual error delta 1 ；
S103: according to the iteration number N and the position residual error delta 1 The final value of the target position is determined.
In a preferred or alternative embodiment: the method in S103 includes:
judging the position residual error delta% and the iteration times N and a preset residual error threshold delta 0 And a preset iteration number set value N 0 To determine a final value for the target location.
In a preferred or alternative embodiment, the position residual delta is determined 1 And the iteration number N and a preset residual error threshold delta 0 And a preset iteration number set value N 0 The method for determining the final value of the target position includes:
e.g. delta 1 Greater than or equal to delta 0 And N is less than or equal to N 0 Returning to S102 and recalculating the calculated accurate value as the initial value in S101;
e.g. delta 1 Less than or equal to delta 0 And N is less than or equal to N 0 The accurate value calculated in S102 is taken as a final value of the target position;
for example, N is greater than or equal to N 0 The initial value of the target position in S101 is taken as the final value of the target position.
Compared with the prior art, the technical scheme provided by the invention has the following beneficial effects:
the invention has the main advantages that the method solves the initial value of the target position of the multi-base sound receiving system by adopting a least square algorithm based on mathematical transformation, performs Taylor series expansion at the initial value, and finally determines the final target settlement result by the number of iteration times and calculation residual errors. The invention avoids the problem of result divergence caused by poor initial value selection of the Taylor series expansion algorithm, and improves the positioning precision of the least square algorithm based on mathematical transformation.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described, it being obvious that the drawings in the description below are only some embodiments of the invention, and that other drawings can be obtained from them without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a GDOP employing a least squares algorithm based on mathematical transformations, according to an embodiment.
FIG. 2 is a schematic diagram of a GDOP employing the present invention.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. The invention may be practiced or carried out in other embodiments that depart from the spirit and scope of the present invention, and the details of the present description may be modified or changed from various points of view and applications. It should be noted that the following embodiments and features in the embodiments may be combined with each other without conflict. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It is noted that various aspects of the embodiments are described below within the scope of the following claims. It should be apparent that the aspects described herein may be embodied in a wide variety of forms and that any specific structure and/or function described herein is merely illustrative. Based on the present disclosure, one skilled in the art will appreciate that one aspect described herein may be implemented independently of any other aspect, and that two or more of these aspects may be combined in various ways. For example, an apparatus may be implemented and/or a method practiced using any number of the aspects set forth herein. In addition, such apparatus may be implemented and/or such methods practiced using other structure and/or functionality in addition to one or more of the aspects set forth herein.
It should also be noted that the drawings provided in the following embodiments merely illustrate the basic concept of the present invention by way of illustration, and only the components related to the present invention are shown in the drawings, not by the number, shape and size of the components in actual implementation, and the form, number and proportion of the components in actual implementation may be arbitrarily changed, and the layout of the components may be more complicated.
In addition, in the following description, specific details are provided in order to provide a thorough understanding of the examples. However, it will be understood by those skilled in the art that aspects may be practiced without these specific details. In order to better understand the aspects of the present invention, the present invention will be described in further detail with reference to the accompanying drawings and detailed description. The terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "first", "" may explicitly or implicitly include one or more of that feature. In the description of the present invention, unless otherwise indicated, the meaning of "a plurality" is two or more.
A method as shown in fig. 1 and 2, comprising:
s101, determining a measurement equation according to each station address in the multi-base sound system, obtaining a linear equation set through mathematical transformation, and obtaining an initial value of a target position through a least square algorithm. The multi-base sound system is a two-dimensional detection system and comprises T-R n And T/R-R n Two types. Where T represents the transmitting station but cannot receive the target echo; T/R represents a transmitting station, which can receive target echoes; r is R n For receiving stations, the upper corner mark n represents the number of receiving stations;
s102, carrying out Taylor series expansion on the measurement equation at the initial value of the target position, and determining the accurate value of the target position, the iteration number N and the position residual error delta 1 ；
S103: and determining the final value of the target position according to the sum position residual error solution. For example, the position residual error Δ is determined 1 And the iteration number N and a preset residual error threshold delta 0 And a preset iteration number set value N 0 To determine the final value of the target position, presetting a residual threshold delta 0 And a preset iteration number set value N 0 The method can be determined according to Monte Carlo simulation experiments, and the following three conditions are compared:
judging the position residual error delta% and the iteration times N and a preset residual error threshold delta 0 And a preset iteration number set value N 0 The method for determining the final value of the target position includes:
e.g. delta 1 Greater than or equal to delta 0 And N is less than or equal to N 0 Returning to S102 and recalculating the calculated accurate value as the initial value in S101;
for example, Δ% is less than or equal to Δ 0 And N is less than or equal to N 0 The accurate value calculated in S102 is taken as a final value of the target position;
for example, N is greater than or equal to N 0 The initial value of the target position in S101 is taken as the final value of the target position.
The invention has the main advantages that the method solves the initial value of the target position of the multi-base sound receiving system by adopting a least square algorithm based on mathematical transformation, performs Taylor series expansion at the initial value, and finally determines the final target settlement result by the number of iteration times and calculation residual errors. The invention avoids the problem of result divergence caused by poor initial value selection of the Taylor series expansion algorithm, and improves the positioning precision of the least square algorithm based on mathematical transformation.
The specific calculation method is as follows:
the simulation analysis of the method of the invention is as follows:
the method is adopted to carry out T-R on a multi-base sound receiving system 2 And (5) performing simulation analysis on the positioning accuracy.
For example, the system includes 1 transmitting station T, coordinates x T ,y T ]And 2 receiving stations Ri, coordinates x Ri ,y Ri ]I=1, 2, the site layout is shown as circles in fig. 2. The equivalent acting distance r=10 km of the receiving station, the base line length d=0.4r, the measurement errors of the transmitting station and the receiving station are consistent, wherein the time measurement error is 25ms, the angle measurement error is 3 degrees, and the site location measurement error is 10m.
(1) Determining a measurement equation according to each station address in the multi-base sound system, obtaining a linear equation set through mathematical transformation, and obtaining a target position initial value through a least square algorithm;
assuming that the target position is [ x, y ], according to the schematic diagram of the positioning principle of the multi-base sonar system given in section 3.3 in the principles and application of multi-base sonar, the following positioning equation is established:
wherein: [ x ] T ,y T ]＝[0,0]i＝1,2。r Σi The total propagation distance, r, of the signal transmitted by the transmitting station after being scattered by the target to the ith receiving station T For the distance of the target from the transmitting station, r Ri For the distance of the target from the ith receiving station, θ Ri A target angle measured for each receiving station.
At present, a set of new solving equations is obtained by carrying out certain mathematical transformation on the measurement equation (1), and positioning solving is carried out by utilizing a least square algorithm, namely, the quadratic term is eliminated in the formula (1) to obtain:
using the measurements of the two receiving base stations to cancel the range of the transmitting station to the target, the following equation is established:
thus, equation (3) can be written in the form of a system of linear equations:
wherein the related coefficient matrix is as follows:
now, the simplified formula (4) is ex=f, and the solution to the target position is completed by using the least square method, which includes:
wherein, the liquid crystal display device comprises a liquid crystal display device,here n=2, the determination of the target initial position is completed.
(2) Carrying out Taylor series expansion on the measurement equation at the initial value of the target position, and solving the target position accurate value, the position residual error and the iteration number N;
the linear least square algorithm based on the Taylor series expansion is an iterative algorithm, and a true value is obtained through iterative calculation of initial coordinates. Assuming that the true position of the target is X (X, y), the initial value in the iterative process isIts deviation from the truth coordinates is delta (deltax, deltay). For measurement equation (1)At the reference point->The Taylor series expansion is performed, and the components above the second order term are ignored. Then there are:
where i=1, 2, represents the measurement equations of the receiving array 1 and the receiving station 2, respectively. The above is deformed to have
Writing the above into matrix form, and writing r Σi (x, y) and θ Ri (x, y) using measured dataAnd->To express, then there are:
Z＝WΔ (8)
wherein:
matrix W is the reference pointJacobi matrix of>
The least square calculation equation of delta is obtained by adopting a pseudo-inverse method:
Δ＝[W T W] -1 W T Z (9)
to reference nodeAs an initial point, the following calculation was performed:
wherein: n is the number of iterations, with an initial value of n=0.
Calculating position residual error delta%:
(3) And giving a final value of the target position according to the position residual error and the iteration times.
Judging position residual error delta% and iteration times N and residual error threshold delta 0 And iteration number set point N 0 If delta%>Δ 0 And N is<N 0 Then go back to step two and calculate the position accuracy value x N+1 y N+1 ]Recalculated as initial value if delta%<Δ 0 And N is<N 0 The position value calculated in the second step is taken as the final value of the target position, if delta%>Δ 0 And N is>N 0 The initial value of the target position in the first step is taken as the final value of the target position, wherein preferably, delta 0 ＝0.001，N 0 ＝4。Δ 0 And N 0 As determined by the Monte Carlo simulation implementation, N is preferably 0 ＝4-6
The accuracy of the positioning of the target by the two-dimensional multi-base sound system can be represented by geometric interpretation of the positioning accuracy (GDOP: geometrical Dilution of Precision), namelyWherein (1)>The position variance is calculated for the target positioning in the x direction and the y direction in the two-dimensional Cartesian coordinate system.
In the embodiment, the measurement errors of the transmitting station and the receiving station in the multi-base system are consistent, wherein the time measurement error is 25ms, the angle measurement error is 3 degrees, and the site location measurement error is 10m. And obtaining a target positioning result by adopting 2000 times of calculation.
The simulation results of the computer are given below, and fig. 1 is a schematic diagram of a GDOP using a least squares algorithm based on mathematical transformation according to an embodiment. FIG. 2 is a schematic diagram of a GDOP employing the present invention. It can be seen from the above that the positioning solution result of the algorithm of the present invention is better in the same region.
The method provided by the invention is described in detail above. The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the core concept of the invention. It should be noted that it will be apparent to those skilled in the art that several improvements and modifications can be made to the invention without departing from the inventive concept, and these improvements and modifications fall within the scope of the appended claims.
Claims (2)
1. An improved method of multi-base sound localization, the method comprising:
s101, determining a measurement equation according to each station address in a multi-base sound system, obtaining a linear equation set through mathematical transformation, and obtaining an initial value of a target position through a least square algorithm;
s102, carrying out Taylor series expansion on the measurement equation at the initial value of the target position, and determining the accurate value of the target position, the iteration number N and the position residual error delta 1 ；
S103: according to the iteration number N and the position residual error delta 1 Determining a final value of the target position by solution, including:
determining position residual delta 1 And the iteration number N and a preset residual error threshold delta 0 And a preset iteration number set value N 0 To determine a final value for the target location, wherein:
e.g. delta 1 Greater than or equal to delta 0 And N is less than or equal to N 0 Returning to S102 and recalculating the calculated accurate value as the initial value in S101;
e.g. delta 1 Less than or equal to delta 0 And N is less than or equal to N 0 The accurate value calculated in S102 is taken as a final value of the target position;
for example, N is greater than or equal to N 0 Taking the initial value of the target position in the step S101 as the final value of the target position;
said delta 0 And N 0 As determined by monte carlo simulation experiments.
2. The method according to claim 1, wherein; said delta 0 ＝0.001，N 0 Ranging from 4 to 6.
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