WO2016206340A1 - 面向矿井运动目标的双标签高精度定位方法 - Google Patents
面向矿井运动目标的双标签高精度定位方法 Download PDFInfo
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- 238000005457 optimization Methods 0.000 claims abstract description 19
- 238000004891 communication Methods 0.000 claims abstract description 3
- 238000012804 iterative process Methods 0.000 claims description 12
- 230000000694 effects Effects 0.000 claims description 4
- 238000010276 construction Methods 0.000 claims description 3
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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
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
-
- E—FIXED CONSTRUCTIONS
- E21—EARTH OR ROCK DRILLING; MINING
- E21F—SAFETY DEVICES, TRANSPORT, FILLING-UP, RESCUE, VENTILATION, OR DRAINING IN OR OF MINES OR TUNNELS
- E21F17/00—Methods or devices for use in mines or tunnels, not covered elsewhere
- E21F17/18—Special adaptations of signalling or alarm devices
-
- 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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/06—Systems determining position data of a target
-
- 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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/52—Discriminating between fixed and moving objects or between objects moving at different speeds
-
- 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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination systems
-
- 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
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/28—Details of pulse systems
- G01S7/285—Receivers
- G01S7/292—Extracting wanted echo-signals
Definitions
- the invention relates to a double label high precision positioning method, in particular to a double label high precision positioning method for a mine moving target.
- the distance between the positioning target and the positioning base station is generally measured by the RSSI method, and then the target position is obtained by a geometric method (such as the trilateral positioning method).
- a geometric method such as the trilateral positioning method.
- the accuracy of the RSSI ranging accuracy is very obvious, resulting in a small accuracy of the ranging, resulting in low accuracy of the single-label mine positioning system, unstable positioning results, and serious positional drift.
- Mine moving targets can be divided into two categories according to their shape.
- the first type of mine moving target is a long strip object parallel to the roadway (such as mine car and shearer); the second type of mine moving target is a long strip perpendicular to the roadway.
- Object such as a person.
- the object of the present invention is to provide a dual-label high-precision positioning method for a mine moving target, which solves the problem that the single-label mine positioning system has low precision, unstable positioning results, and serious positional drift.
- the dual-label high-precision positioning method comprises: a first type of mine moving target positioning method and a second type of mine moving target positioning method; the method installs two positions horizontally or vertically on the moving target Labeling and communicating with two positioning base stations installed along the roof of the roadway, and constructing a position of the moving target in real time by constructing an optimization function between the tag and the positioning base station RSSI distance and the estimated distance and solving the minimum value;
- the first type of mine moving target positioning method one positioning label U 1 and U 2 are installed on each of the head and the tail of the target to be positioned, and the distance between the positioning labels U 1 and U 2 is represented by L; tab to know the location of the target in the roadway; each tag can be mounted simultaneously with the two tunnel roof line positioning station B 1 and B 2 communication, the positioning station B 1 and B is connected to the straight line constituting the two points B 1 2 B 2 , the positioning feet U 1 and U 2 to the straight line B 1 B 2 are respectively P 1 and P 2 ,
- H is the height of the label to the center of the top plate;
- the target is neglected in the width dimension of the roadway, and is modeled as one-dimensional positioning.
- the two points of the positioning labels U 1 and U 2 are connected to form a straight line U 1 U 2 , with the straight line U 1 U 2 as the horizontal axis and the abscissa of U 1 .
- the abscissa of U 2 is x+L;
- the vertical axis is the direction upward with the sub-plane in the longitudinal direction of the roadway;
- the x opt value under the condition to achieve the target's positioning is the x opt value under the condition to achieve the target's positioning.
- the positioning result is an unbiased estimate, then
- the position x opt can be obtained by solving the x value that minimizes f(x):
- the iteration encounters the following conditions: (1) the number of iterations exceeds the threshold N, and the entire iterative process terminates; (2) if but Then the rightward iteration ends, only the leftward iteration; if but Then the left iteration ends and only the right iteration is performed; (3) And The entire iterative process terminates; (4) When f(x) ⁇ f th , the entire iterative process terminates, where f th is the given distance error threshold.
- the second type of mine moving target the steps are as follows:
- the method installs two positioning tags horizontally or vertically on a moving target, and communicates with two positioning base stations installed along the roof of the roadway, by constructing a tag and positioning the base station RSSI distance from the estimated distance
- the optimization function solves the minimum value and obtains the position of the moving target in real time.
- the optimization function is solved in an iterative manner, which includes two steps: iterative initial value determination and left/right iteration.
- Overcoming the single-label positioning is affected by the large environmental factors of the mine, significantly improving the positioning accuracy.
- These equipment and personnel can fully install two or more positioning tags, and use the space constraints between multiple tags to improve positioning accuracy.
- the invention solves the problem that the single-label mine positioning system has low precision, the positioning result is unstable, and there is a serious position drift problem, and the object of the invention is achieved.
- the invention adopts the double label method for positioning the mine moving target, and only needs to add a positioning label on the target to be positioned to greatly improve the positioning accuracy, the upgrade cost is low, the deployment is easy, and the long strip object parallel to the roadway is suitable. (such as mine cars, shearers), also applies to long strips (such as personnel) perpendicular to the roadway.
- 1 is a double label positioning map of a first type of mine moving target of the present invention.
- FIG. 2 is a double label positioning map of a second type of mine moving target of the present invention.
- the dual-label high-precision positioning method includes: a first type of mine moving target positioning method and a second type of mine moving target positioning method; the method installs two positioning labels horizontally or vertically on the moving target, and The two positioning base stations installed in the roof of the roadway communicate, and the position of the moving target is obtained in real time by constructing an optimization function between the tag and the positioning base station RSSI distance and the estimated distance and solving the minimum value;
- the first type of mine moving target positioning method one positioning label U 1 and U 2 are installed on the head and the tail of the target to be positioned, and the distance between the positioning labels U 1 and U 2 is represented by L; and any one of the labels is positioned. to know the location of the target in the roadway; each tag can communicate simultaneously mounting two midline positioning tunnel roof and the base station B 1 and B 2, the positioning station B 1 and B 2 are attached to two points constitute a straight line B 1 B 2 , the positioning feet U 1 and U 2 to the straight line B 1 B 2 are respectively P 1 and P 2 ,
- H is the height of the label to the center of the top plate; The dimension dimension in the roadway is neglected, and is modeled as one-dimensional positioning.
- the two points of the positioning labels U 1 and U 2 are connected to form a straight line U 1 U 2 , with the straight line U 1 U 2 as the horizontal axis and the abscissa of U 1 as the x coordinate.
- the horizontal coordinate of U 2 is x+L;
- the vertical axis is the upward direction with the dividing plane in the longitudinal direction of the roadway;
- the x opt value under the condition to achieve the target's positioning is the x opt value under the condition to achieve the target's positioning.
- the positioning result is an unbiased estimate, then
- the position x opt can be obtained by solving the x value that minimizes f(x):
- the iteration encounters the following conditions: (1) the number of iterations exceeds the threshold N, and the entire iterative process terminates; (2) if but Then the rightward iteration ends, only the leftward iteration; if but Then the left iteration ends and only the right iteration is performed; (3) And The entire iterative process terminates; (4) When f(x) ⁇ f th , the entire iterative process terminates, where f th is the given distance error threshold.
- the second type of mine moving target the steps are as follows:
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Abstract
一种面向矿井运动目标的双标签高精度定位方法,属于双标签高精度定位方法。该双标签高精度定位方法包括:第一类矿井运动目标定位方法和第二类矿井运动目标定位方法;所述方法在运动目标上水平或垂直安装两个定位标签(U 1 ,U 2),并与沿巷道顶板安装的两个定位基站(B 1,B 2)通信,通过构造标签(U 1 ,U 2)与定位基站(B 1,B 2)RSSI距离与估计距离之间的优化函数并求解其最小值,实时得到运动目标的位置;优化函数的求解通过迭代的方式完成,它包括迭代初值确定、左/右迭代两个主要步骤。仅需在待定位目标上添加一个定位标签即可大幅提高定位精度,升级成本低,部署容易,适合于与巷道平行的长条状对象(如矿车、采煤机),也适用于与巷道垂直的长条状对象(如人员)。
Description
本发明涉及一种双标签高精度定位方法,特别是一种面向矿井运动目标的双标签高精度定位方法。
在现有矿井定位系统中,一般通过RSSI的方式测得定位目标与定位基站之间的距离,然后通过几何的方法(如三边定位法)求得目标位置。然而,RSSI测距的精确度后衰落效应的影响非常明显,致使测距精度很小,致使采用单标签的矿井定位系统的精度低下,定位结果不稳定,存在严重的位置漂移。
矿井运动目标可根据其外形分成两类,第一类矿井运动目标是与巷道平行的长条状对象,(如矿车、采煤机);第二类矿井运动目标是与巷道垂直的长条状对象,(如人员)。
发明内容
本发明的目的是要提供一种面向矿井运动目标的双标签高精度定位方法,解决单标签的矿井定位系统的精度低下,定位结果不稳定,存在严重的位置漂移的问题。
本发明的目的是这样实现的:该双标签高精度定位方法包括:第一类矿井运动目标定位方法和第二类矿井运动目标定位方法;所述方法在运动目标上水平或垂直安装两个定位标签,并与沿巷道顶板安装的两个定位基站通信,通过构造标签与定位基站RSSI距离与估计距离之间的优化函数并求解其最小值,实时得到运动目标的位置;
所述第一类矿井运动目标定位方法:在待定位目标的头部和尾部各安装一个定位标签U1和U2,定位标签U1和U2之间的距离用L表示;定位出任何一个标签,即可知道目标在巷道中的位置;每个标签都能同时与两个安装巷道顶板中线的定位基站B1和B2通信,将定位基站B1和B2二点相连构成直线B1B2,定位标签U1和U2到直线B1B2的垂足分别为P1和P2,|U1P1|=|U2P2|=H为标签到顶板中心的高度;目标在巷道中宽度维上忽略不计,建模为一维定位,将定位标签U1和U2二点相连构成直线U1U2,以直线U1U2为横轴,U1的横坐标为x,则U2的横坐标为x+L;纵轴为与巷道纵向中分平面向上的方向;求解出x在满足
xopt=min f(x)
条件下的xopt值,实现目标的定位。
所述第一类矿井运动目标定位方法的具体定位过程:
1)在待定位目标的头部和尾部各安装一个定位标签U1和U2;
2)构造优化函数
定位基站的坐标(xB,H)和(xB+LB,H)、基站之间的距离|B1B2|=LB是已知的;当定位标
签U1和U2的坐标分别为(x,0)和(x+L,0);xB≤x≤xB+LB;设B1与定位标签U1和U2的距离分别为d11和d12,B2与定位标签U1和U2的距离分别为d21和d22,∠B1U1P1=θ,∠P1U1B2=α;
构造优化函数f(x):
(1)式右边先平方再开方的目的是为了保证每一项都为正,以免求和的时候正负抵消;其中,为标签Ui,i=1,2的坐标,且
为定位基站Bj,j=1,2的坐标,且这些量中,是已知条件,dij可用RSSI的方式得到;节点i、j之间的RSS值遵循对数正态阴影模型:
于是,(1)式只有x未知。将U1、U2、B1、B2和dij代入(1)式,得:
如果定位结果是无偏估计,则|UiBj|=dij,从而使得f(x)=0;如果是有偏估计,应取能够使得f(x)最小的x,即待定位目标位置xopt可以通过求解使得f(x)最小的x值获得:
xopt=min f(x) (5)
3)优化函数的求解
(1)通过单标签矿井目标定位方法获得迭代初值x0,
sinθ=(x-xB)/d11,cosθ=H/d11,sinα=(xB+LB-x)/d21,cosα=H/d21,
cosα=H/d21,sinα=(xB+LB-x)/d21,因此,
针对ΔB1U1B2,根据余弦定理,有:
利用一元二次方程求根公式解方程(7),并令其为迭代初值x0,得:
(2)通过双向迭代法获得最优解
以x0为起始点,令xi+1=xi±Δx,i=0,1,2,…,N,代入(4)式求得第i+1次迭代的f(x)值fi+1(xi);其中,N为预设的最大迭代次数,Δx为迭代步长,若Δx取正号,则向B2的方向迭代(右向迭代),反之则向B1的方向迭代即左向迭代;迭代起始的时候,xopt=x0;在迭代过程中,若fi+1(xi)>fi(xi),则令xopt=xi+1,否则保持不变;为了加快迭代速度,这里同时进行双向迭代;令分别对应右向迭代和左向迭代;
迭代遇到下列条件结束:(1)超过迭代次数超过阈值N,整个迭代过程终止;(2)若但则右向迭代结束,只进行左向迭代;若但则左向迭代结束,只进行右向迭代;(3)且整个迭代过程终止;(4)当f(x)≤fth的时候,整个迭代过程终止,其中fth是给定的距离误差阈值。
所述第二类矿井运动目标,步骤如下:
1)分别在待定位目标的头部、中部各安装一个定位标签U1和U2,并令|U1U2|=L,U1到B1B2的垂足P的距离|U1P|=H,|B1B2|=LB;
2)构造优化函数,待定位目标位置xopt=min f(x);
3)最优解的求解:
(2)通过双向迭代法获得最优解xopt。
有益效果,由于采用了上述方案,该方法在运动目标上水平或垂直安装两个定位标签,并与沿巷道顶板安装的两个定位基站通信,通过构造标签与定位基站RSSI距离与估计距离之间的优化函数并求解其最小值,实时得到运动目标的位置。优化函数的求解通过迭代的方式完成,它包括迭代初值确定、左/右迭代两个步骤。克服单标签定位受矿井环境因素较大的缺陷,显著提高定位精度。这些装备和人员完全可以安装两个甚至多个定位标签,利用多个标签之间的空间约束提高定位精度。解决了单标签的矿井定位系统的精度低下,定位结果不稳定,存在严重的位置漂移的问题,达到了本发明的目的。
优点:本发明采用双标签的方法进行矿井运动目标定位,仅需在待定位目标上添加一个定位标签即可大幅提高定位精度,升级成本低,部署容易,适合于与巷道平行的长条状对象(如矿车、采煤机),也适用于与巷道垂直的长条状对象(如人员)。
图1是本发明的第一类矿井运动目标双标签定位图。
图2是本发明的第二类矿井运动目标双标签定位图。
实施例1:该双标签高精度定位方法包括:第一类矿井运动目标定位方法和第二类矿井运动目标定位方法;所述方法在运动目标上水平或垂直安装两个定位标签,并与沿巷道顶板安装的两个定位基站通信,通过构造标签与定位基站RSSI距离与估计距离之间的优化函数并求解其最小值,实时得到运动目标的位置;
第一类矿井运动目标定位方法:在待定位目标的头部和尾部各安装一个定位标签U1和U2,定位标签U1和U2之间的距离用L表示;定位出任何一个标签,即可知道目标在巷道中的位置;每个标签都能同时与两个安装巷道顶板中线的定位基站B1和B2通信,将定位基站B1和B2二点相连构成直线B1B2,定位标签U1和U2到直线B1B2的垂足分别为P1和P2,|U1P1|=|U2P2|=H为标签到顶板中心的高度;目标在巷道中宽度维上忽略不计,建模为一维定位,将定位标签U1和U2二点相连构成直线U1U2,以直线U1U2为横轴,U1的横坐标为x,则U2的横坐标为x+L;纵轴为与巷道纵向中分平面向上的方向;求解出x在满足
xopt=min f(x)
条件下的xopt值,实现目标的定位。
所述第一类矿井运动目标定位方法的具体定位过程:
1)在待定位目标的头部和尾部各安装一个定位标签U1和U2;
2)构造优化函数
定位基站的坐标(xB,H)和(xB+LB,H)、基站之间的距离|B1B2|=LB是已知的;当定位标签U1和U2的坐标分别为(x,0)和(x+L,0);xB≤x≤xB+LB;设B1与定位标签U1和U2的距离分别为d11和d12,B2与定位标签U1和U2的距离分别为d21和d22,∠B1U1P1=θ,∠P1U1B2=α;
构造优化函数f(x):
(1)式右边先平方再开方的目的是为了保证每一项都为正,以免求和的时候正负抵消;其中,为标签Ui,i=1,2的坐标,且
为定位基站Bj,j=1,2的坐标,且这些量中,是已知条件,dij可用RSSI的方式得到;节点i、j之间的RSS值遵循对数正态阴影模型:
于是,(1)式只有x未知。将U1、U2、B1、B2和dij代入(1)式,得:
如果定位结果是无偏估计,则|UiBj|=dij,从而使得f(x)=0;如果是有偏估计,应取能够使得f(x)最小的x,即待定位目标位置xopt可以通过求解使得f(x)最小的x值获得:
xopt=min f(x) (5)
3)优化函数的求解
(1)通过单标签目标定位方法获得迭代初值x0,
在图1中,sinθ=(x-xB)/d11,cosθ=H/d11,sinα=(xB+LB-x)/d21,cosα=H/d21,因此,
cosα=H/d21,sinα=(xB+LB-x)/d21,因此,
针对ΔB1U1B2,根据余弦定理,有:
利用一元二次方程求根公式解方程(7),并令其为迭代初值x0,得:
(2)通过双向迭代法获得最优解
以x0为起始点,令xi+1=xi±Δx,i=0,1,2,…,N,代入(4)式求得第i+1次迭代的f(x)值fi+1(xi);其中,N为预设的最大迭代次数,Δx为迭代步长,若Δx取正号,则向B2的方向迭代(右向迭代),反之则向B1的方向迭代即左向迭代;迭代起始的时候,xopt=x0;在迭代过程中,若fi+1(xi)>fi(xi),则令xopt=xi+1,否则保持不变;为了加快迭代速度,这里同时进行双向迭代;令分别对应右向迭代和左向迭代;
迭代遇到下列条件结束:(1)超过迭代次数超过阈值N,整个迭代过程终止;(2)若但则右向迭代结束,只进行左向迭代;若但则左向迭代结束,只进行右向迭代;(3)且整个迭代过程终止;(4)当f(x)≤fth的时候,整个迭代过程终止,其中fth是给定的距离误差阈值。
所述第二类矿井运动目标,步骤如下:
1)分别在待定位目标的头部、中部各安装一个定位标签U1和U2,并令|U1U2|=L,U1到B1B2的垂足P的距离|U1P|=H,|B1B2|=LB;
2)构造优化函数,待定位目标位置xopt=min f(x);
3)最优解的求解:
(2)通过双向迭代法获得最优解xopt。
Claims (2)
- 一种面向矿井运动目标的双标签高精度定位方法,其特征是:该双标签高精度定位方法包括:第一类矿井运动目标定位方法和第二类矿井运动目标定位方法;所述方法在运动目标上水平或垂直安装两个定位标签,并与沿巷道顶板安装的两个定位基站通信,通过构造标签与定位基站RSSI距离与估计距离之间的优化函数并求解其最小值,实时得到运动目标的位置;所述第一类矿井运动目标定位方法:在待定位目标的头部和尾部各安装一个定位标签U1和U2,定位标签U1和U2之间的距离用L表示;定位出任何一个标签,即可知道目标在巷道中的位置;每个标签都能同时与两个安装巷道顶板中线的定位基站B1和B2通信,将定位基站B1和B2二点相连构成直线B1B2,定位标签U1和U2到直线B1B2的垂足分别为P1和P2,|U1P1|=|U2P2|=H为标签到顶板中心的高度;目标在巷道中宽度维上忽略不计,建模为一维定位,将定位标签U1和U2二点相连构成直线U1U2,以直线U1U2为横轴,U1的横坐标为x,则U2的横坐标为x+L;纵轴为与巷道纵向中分平面向上的方向;求解出x在满足xopt=min f(x)条件下的xopt值,实现目标的定位;所述第二类矿井运动目标,步骤如下:1)分别在待定位目标的头部、中部各安装一个定位标签U1和U2,并令|U1U2|=L,U1到B1B2的垂足P的距离|U1P|=H,|B1B2|=LB;2)构造优化函数,待定位目标位置xopt=min f(x);3)最优解的求解:(2)通过双向迭代法获得最优解xopt。
- 根据权利要求1所述的面向矿井运动目标的双标签高精度定位方法,其特征是:所述第一类矿井运动目标定位方法的具体定位过程:1)在待定位目标的头部和尾部各安装一个定位标签U1和U2;2)构造优化函数定位基站的坐标(xB,H)和(xB+LB,H)、基站之间的距离|B1B2|=LB是已知的;当定位标签U1和U2的坐标分别为(x,0)和(x+L,0);xB≤x≤xB+LB;设B1与定位标签U1和U2的距离分别为d11和d12,B2与定位标签U1和U2的距离分别为d21和d22,∠B1U1P1=θ,∠P1U1B2=α;构造优化函数f(x):(1)式右边先平方再开方的目的是为了保证每一项都为正,以免求和的时候正负抵消;其中,为标签Ui,i=1,2的坐标,且于是,(1)式只有x未知。将U1、U2、B1、B2和dij代入(1)式,得:如果定位结果是无偏估计,则|UiBj|=dij,从而使得f(x)=0;如果是有偏估计,应取能够使得f(x)最小的x,即待定位目标位置xopt可以通过求解使得f(x)最小的x值获得:xopt=min f(x) (5)3)优化函数的求解(1)通过单标签矿井目标定位方法获得迭代初值x0,sinθ=(x-xB)/d11,cosθ=H/d11,sinα=(xB+LB-x)/d21,cosα=H/d21,cosα=H/d21,sinα=(xB+LB-x)/d21,因此,针对ΔB1U1B2,根据余弦定理,有:利用一元二次方程求根公式解方程(7),并令其为迭代初值x0,得:(2)通过双向迭代法获得最优解以x0为起始点,令xi+1=xi±Δx,i=0,1,2,…,N,代入(4)式求得第i+1次迭代的f(x)值fi+1(xi);其中,N为预设的最大迭代次数,Δx为迭代步长,若Δx取正号,则向B2的方向迭代(右向迭代),反之则向B1的方向迭代即左向迭代;迭代起始的时候,xopt=x0;在迭代过程中,若fi+1(xi)>fi(xi),则令xopt=xi+1,否则保持不变;为了加快迭代速度,这里同时进行双向迭代;令分别对应右向迭代和左向迭代;
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