CN111398896B - False point removal preprocessing method based on datum line pairwise crossing positioning point distance - Google Patents
False point removal preprocessing method based on datum line pairwise crossing positioning point distance Download PDFInfo
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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
- G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
Abstract
The invention relates to a false point removal preprocessing method based on a reference line pairwise crossing positioning point distance, which forms a double-station crossing positioning point set; taking a certain sight vector of a certain station A as a datum line, taking a cross locating point of the certain sight vector of another station B as a datum point, and calculating a paired cross locating point set of a station C corresponding to the datum line; judging whether the reference point is a false point or not by using the distance of the paired crossed locating points, and if so, removing the reference point from the set of the two-station crossed locating points; traversing all the reference points corresponding to all the reference lines, and repeatedly executing the second step and the third step; and the preprocessed double-station cross positioning points are aggregated and used for subsequent data association, so that the data association efficiency is improved, and the interference of false points is reduced. The invention utilizes the false point preprocessing method based on the distance of the datum line pairwise crossing positioning points to remove a large number of false points and reduce the computational complexity of subsequent data processing.
Description
Technical Field
The invention relates to a false point removal preprocessing method, in particular to a false point removal preprocessing method based on a datum line pairwise crossing positioning point distance, and belongs to the technical field of electronic reconnaissance.
Background
The passive positioning is a key technology of a passive detection system, the used reconnaissance receiver does not emit electromagnetic signals, only utilizes the received electromagnetic signals to detect targets, and has higher system operating distance while ensuring concealment. Nowadays, the electromagnetic environment is increasingly complex, electromagnetic signals on a battlefield are more complex and changeable, and how to accurately estimate the position of a target radiation source and realize accurate striking is always the key point of research of scholars at home and abroad. The direction-finding cross positioning utilizes angle information with high measurement precision to carry out cross positioning, has simple principle and high processing speed, and is an effective passive positioning method in a complex and changeable electromagnetic environment.
Since the measurement station simultaneously obtains the sight vector (angle) data of a plurality of radiation source targets, which sight vector data of a plurality of stations come from the same target cannot be automatically distinguished, and a wrong association phenomenon is generated, so that a large number of false point targets appear. When the number of targets increases, the false dot phenomenon becomes more serious. Typical false point removal methods include clustering and data correlation.
The clustering method takes a set of double-station cross positioning points traversing all different stations as a sample space, and divides the sample space into different clusters by the existing clustering algorithm according to the characteristics of distance, density and the like. And then according to the characteristics of the point number, the distance between points, the density and the like of each cluster, eliminating the clusters corresponding to the false points, and leaving the clusters corresponding to the real targets.
And traversing all possible sight line vector combinations by a data association method, carrying out confidence evaluation on various combinations, taking the positioning intersection corresponding to the combination with the highest confidence as a real target position, and considering the positioning intersections corresponding to the other combinations as false points. The data correlation method has high reliability but high computational complexity. When the number of targets increases, the NP-hard problem that the computational complexity increases exponentially is faced, and the real-time performance cannot be guaranteed.
Both methods need to be preprocessed to reduce the sample space or the number of combinations, namely, the false point interference is reduced, and the robustness of a subsequent clustering or data association method is improved; and meanwhile, the computational complexity of subsequent clustering or data association is greatly reduced.
Disclosure of Invention
The invention aims to provide a false point removal preprocessing method based on a distance between paired crossing positioning points of reference lines, aiming at solving the problem of the existing false point removal method for multi-site and multi-target passive positioning.
The purpose of the invention is realized as follows:
a false point removal preprocessing method based on the distance of paired crossing positioning points of reference lines comprises the following steps:
the method comprises the following steps: selecting different sight vector samples of two different sites, giving a double-site cross positioning result, traversing all data association combinations, and forming a double-site cross positioning point set;
step two: taking a certain sight vector of a certain station A as a datum line, taking a cross locating point of the certain sight vector of another station B as a datum point, and calculating a paired cross locating point set of a station C corresponding to the datum line; site C is any one of the third sites except the A, B site;
step three: judging whether the reference point is a false point or not by using the distance of the paired crossed locating points, and if so, removing the reference point from the set of the two-station crossed locating points;
step four: traversing all the reference points corresponding to all the reference lines, and repeatedly executing the second step and the third step;
step five: and the preprocessed double-station cross positioning points are aggregated and used for subsequent data association, so that the data association efficiency is improved, and the interference of false points is reduced.
The invention also includes such features:
1. the first step is specifically as follows:
a total of NS measurement stations are known, their coordinates being: (x)1,y1)、(x2,y2)、...、(xNS,yNS) Assume there are NT radiation source targets to measure site A (x)i,yi) And site B (x)j,yj) The direction-finding cross positioning is carried out on the nth radiation source,
suppose that the azimuth angles of the two measurement stations to the nth target are respectively thetaAn、θBnThen, according to the geometric relationship between the nth target and the two sites, the target coordinates can be estimated:
obtaining the estimated coordinates of the nth radiation source target
And traversing all the data association combinations to form a double-station cross positioning point set X.
2. The second step is specifically as follows: the intersection positioning point of a certain sight vector datum line of a certain station A and a certain sight vector of another station B is a reference point P, and the intersection positioning point of the sight vector of a station C and the datum line is PiNT, NT being the target number, (P, P)i) Called pairwise crossing anchor points, all (P, P)i) NT form a set of paired intersection anchor point sets;
if only one site is available except for the site A and the site B, one reference point corresponds to a set of paired crossed positioning point sets; if there are a plurality of sites besides the site a and the site B, one reference point corresponds to a plurality of sets of paired cross anchor points, and each site except A, B generates a set of paired cross anchor points with the reference point.
3. The third step is specifically as follows:
(1) if only three sites exist, each reference point only corresponds to one group of paired crossed positioning point sets, and the Euclidean distance between two points of each paired crossed positioning point in the paired crossed positioning point sets is calculated; finding out the pairwise cross positioning point with the minimum distance to obtain the minimum Euclidean distance dmin(ii) a Calculating an azimuth angle value of a connecting line of the reference point and the third station, and adding two azimuth angle values corresponding to two sight line vectors forming the reference point to obtain three azimuth angle values; calculating to obtain a distance threshold value d according to the three azimuth angle values and the set false point false rejection rate betath(ii) a When d isminGreater than a distance threshold dthIf so, the reference point P is considered as a false point, and is deleted; otherwise, the point is a real point;
(2) if more than three sites exist, each reference point corresponds to a plurality of groups of paired crossed positioning point sets, each group of paired crossed positioning point sets has a minimum Euclidean distance, the steps in b, c and d are repeated, and as long as the minimum Euclidean distance corresponding to one group of paired crossed positioning point sets is larger than a distance threshold dthIf the reference point P is a false point, deleting the reference point P; otherwise, the data is retained.
4. The distance threshold dthThe calculation method of (2) is as follows:
a. let P and P' form a pair of crossed positioning points, and the crossed positioning points are formed by correctly associated sight line vectors, and the reference point P is an azimuth angle thetaAAnd azimuth angle thetaBThe determined estimated point, P', is determined by the azimuth angle thetaAAnd azimuth angle thetaCIs determined where thetaA、θB、θCAzimuth observations (random variables) corresponding to the same target for each site A, B, C;
b. the coordinates of the point P and the point P' are represented by thetaA、θB、θCCan be determined according to the cross-location equation; calculating the distance function d between the point P and the point P' according to the coordinatesAB_ACDistance function with argument as azimuth observation: dAB_AC＝f(θA,θB,θC)；
c. F (theta)A,θB,θC) First order Taylor expansion is performed at three azimuthal values, approximated as
d. Is calculated to obtain
Mean μ and variance σ of2Wherein the azimuth angle theta is assumedA、θB、θCObey Gaussian distribution, variance, respectively(accuracy of angle measurement)
The method comprises the following steps of (1) knowing;
e. setting false point error rejection rate beta, i.e.
Satisfies the following conditions:
solving an equation solution with the following independent variable as a distance variable d:
where erf (x) is a function of the error,
solution of the equation, i.e. the distance threshold dth。
Compared with the prior art, the invention has the beneficial effects that:
the invention discloses a false point preprocessing and removing method based on a datum line pairwise crossing positioning point distance. The method deletes a large number of false points by using the distance threshold, remarkably reduces related candidate data association combinations or sample space point numbers, and can be used for the false point pretreatment of various types of data association methods. The method can effectively reduce the false point interference, improve the efficiency of subsequent data association and is beneficial to improving the accuracy of data association.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic view of a direction-finding cross-location;
fig. 3 is an explanatory diagram of the paired intersection anchor points of the three-site and five-target.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The basic idea of the invention is as follows: and taking the sight line vector of one measuring station as a reference line, and carrying out cross positioning with a certain sight line vector of another station to obtain a reference point. And calculating a set of crossed positioning points formed by all sight line vectors of the third station and the reference line respectively. If the reference point is a real target, the condition of missed detection of direction finding reconnaissance is not considered, a cross positioning point corresponding to the same real target as the reference point is necessarily arranged in the set, the distance between the cross positioning point and the reference point is always the minimum, and the distance is smaller than a certain distance threshold value with high probability. Based on the principle, the invention calculates the distances between the reference points and all the points in the set by pairwise crossing positioning points one by one. If the distance of the minimum paired crossed positioning points is still larger than a certain distance threshold, the reference point is judged to be a false point, and a crossed positioning point sample set or a data association combination is removed.
The invention aims to be realized by the following technical scheme:
a multi-target passive positioning false point removing method based on a reference line pairwise crossing positioning point distance specifically comprises the following steps:
step one, selecting different sight vector samples of two different stations optionally, and giving a double-station cross positioning result. And traversing all the data association combinations to form a double-station cross positioning point set X. A total of NS measurement stations are known, their coordinates being: (x)1,y1)、(x2,y2)、...、(xNS,yNS) Assume that there are NT radiation source targets. To measure site A (x)i,yi) And site B (x)j,yj) And carrying out direction-finding cross positioning on the nth radiation source.
Suppose that the azimuth angles of the two measurement stations to the nth target are respectively thetaAn、θBn. Then, based on the geometric relationship between the nth target and the two sites, the target coordinates can be estimated:
obtaining the estimated coordinates of the nth radiation source target
And traversing all the data association combinations to form a double-station cross positioning point set X.
And step two, taking a certain sight vector of a certain measuring station A as a reference line and the intersection positioning point of the certain sight vector of another station B as a reference point, and calculating a paired intersection positioning point set of a station C (any one third station except A, B stations) corresponding to the reference point.
The intersection positioning point of a certain sight vector datum line of a certain station A and a certain sight vector of another station B is a reference point P, and the intersection positioning point of the sight vector of a station C and the datum line is PiNT, NT is the target number. (P, P)i) Called pairwise crossing anchor points, all (P, P)i) NT constitutes a set of pairwise intersecting anchor points.
If only one site is available except for the site A and the site B, one reference point corresponds to a set of paired crossed positioning point sets; if there are a plurality of sites besides the site a and the site B, one reference point corresponds to a plurality of sets of paired cross anchor points, and each site except A, B generates a set of paired cross anchor points with the reference point.
And step three, judging whether the reference point is a false point or not by using the distance between the paired cross positioning points, and if so, removing the reference point from the set of the double-station cross positioning points.
(1) If there are only three sites, each reference point only corresponds to a set of paired crossed anchor points. Calculating Euclidean distance between two points of each paired crossed positioning point in the paired crossed positioning point set, and finding out minimum Euclidean distance dmin(ii) a Calculating the azimuth angle value of the connecting line of the reference point and the third station, and adding two azimuth angle values corresponding to two sight line vectors forming the reference point to obtain three azimuth anglesA value of the metric; calculating a distance threshold value d based on the three azimuth angle values and the set false point false rejection rate betath(ii) a When d isminGreater than a distance threshold dthIf so, the reference point P is considered as a false point, and the reference point is deleted; otherwise, the data is retained.
(2) If more than three sites exist, each reference point corresponds to a plurality of groups of paired crossed positioning point sets, and each group of paired crossed positioning point sets has a minimum Euclidean distance. As long as the minimum Euclidean distance corresponding to a set of paired crossed positioning point sets is larger than the corresponding distance threshold value dthIf the reference point P is a false point, deleting the reference point; otherwise, the data is retained.
(3) Distance threshold dthThe calculation method of (2) is as follows:
a. let P and P' form a pair of crossed positioning points, and the crossed positioning points are formed by correctly associated sight line vectors, and the reference point P is an azimuth angle thetaAAnd azimuth angle thetaBThe determined estimated point, P', is determined by the azimuth angle thetaAAnd azimuth angle thetaCAnd (4) determining. Wherein theta isA、θB、θCAzimuth observations (random variables) corresponding to the same target for each site A, B, C;
b. the coordinates of the point P and the point P' are represented by thetaA、θB、θCCan be determined according to the cross-location equation; calculating the distance function d between the point P and the point P' according to the coordinatesAB_ACDistance function with argument as azimuth observation: dAB_AC＝f(θA,θB,θC)；
c. F (theta)A,θB,θC) Performing first-order Taylor expansion at the three azimuth angle values obtained in step three (1), and approximating to
d. Is calculated to obtain
Mean μ and variance σ of2Wherein the azimuth angle theta is assumedA、θB、θCObeying Gaussian distribution, variance (angular accuracy)
The method comprises the following steps of (1) knowing;
e. setting false point error rejection rate beta, i.e.
Satisfies the following conditions:
solving an equation solution with the following independent variable as a distance variable d:
where erf (x) is a function of the error,
solution of the equation, i.e. the distance threshold dth。
And step four, traversing all the reference points corresponding to all the reference lines, and repeatedly executing the second step and the third step. The step has two cyclic variables, one is to traverse all reference points corresponding to each datum line; secondly, all the reference lines are traversed, namely all the sight line vectors are taken as the reference lines in turn.
And step five, the preprocessed double-station cross positioning point set without a large number of false points is used for subsequent data association, so that the data association efficiency is improved, and the interference of the false points is reduced.
Examples
As shown in fig. 1, the specific implementation steps of the present invention are as follows:
step one, as shown in the direction-finding cross-positioning principle of fig. 2, a total of NS measurement stations are known, and their coordinates are: (x)1,y1)、(x2,y2)、...、(xNS,yNS) Assume that there are NT radiation source targets. To measure site A (x)i,yi) And stationPoint B (x)j,yj) And carrying out direction-finding cross positioning on the nth radiation source.
Suppose that the azimuth angles of the two measurement stations to the nth target are respectively thetaAn、θBn. Then, based on the geometric relationship between the nth target and the two sites, the target coordinates can be estimated:
the estimated coordinates of the nth radiation source target can be obtained
In this embodiment, NS is 3 and NT is 5. And traversing all the data association combinations to form a double-station cross positioning point set under the conditions of three stations and five targets.
And step two, calculating a paired crossed positioning point set of the station corresponding to the reference point.
As shown in fig. 3, P is the reference point, (P, P)1) A pair of cross positioning points (P, P) as a reference point2)、(P,P3)、...、(P,P5) Are all paired intersection anchor points. They constitute a set of paired intersecting anchor points for the fiducial. There are three observers in this scenario, so each fiducial point corresponds to a set of paired intersecting anchor point sets.
And step three, judging whether the reference points are false points or not by using the distances of the paired crossed positioning points.
(1) If there are only three sites, each reference point only corresponds to a set of paired crossed anchor points. Calculating Euclidean distance between two points of each paired crossed positioning point in the paired crossed positioning point set, and finding out minimum Euclidean distance dmin(ii) a Calculating the azimuth angle value of the connecting line of the reference point and the third station, and adding two sight line vectors forming the reference pointObtaining three azimuth angle values by the corresponding two azimuth angle values, and respectively recording the three azimuth angle values as
Calculating a distance threshold value d based on the three azimuth angle values and the set false point false rejection rate betath(ii) a . When d isminGreater than a distance threshold dthIf so, the reference point P is considered as a false point, and the reference point is deleted; otherwise, the data is retained.
(2) If more than three sites exist, each reference point corresponds to a plurality of groups of paired crossed positioning point sets, and each group of paired crossed positioning point sets has a minimum Euclidean distance. As long as the minimum Euclidean distance corresponding to a set of paired crossed positioning point sets is larger than the corresponding distance threshold value dthIf the reference point P is a false point, deleting the reference point; otherwise, the data is retained.
(3) Distance threshold dthThe calculation method of (2) is as follows:
let P and P' form a pair of crossed positioning points, and the crossed positioning points are formed by correctly associated sight line vectors, and the reference point P is an azimuth angle thetaAAnd azimuth angle thetaBThe determined estimated point, P', is determined by the azimuth angle thetaAAnd azimuth angle thetaCAnd (4) determining. Wherein theta isA、θB、θCAzimuth observations (random variables) corresponding to the same target for each site A, B, C;
the coordinates of the point P and the point P' are represented by thetaA、θB、θCCan be determined according to the cross-location equation; calculating the distance function d between the point P and the point P' according to the coordinatesAB_ACDistance function with argument as azimuth observation: dAB_AC＝f(θA,θB,θC)；
F (theta)A,θB,θC) Performing a first order Taylor expansion at the three azimuthal observations obtained in step three (1), approximating
Setting false point error rejection rate beta, i.e.
Satisfies the following conditions:
solving an equation solution with the following independent variable as a distance variable d:
where erf (x) is a function of the error,
solution of the equation, i.e. the distance threshold dthBeta may be set to a number generally between 0.01 and 0.05.
And step four, traversing the reference points corresponding to all the reference lines (corresponding to 15 reference lines in a three-site and five-target simulation scene, and corresponding to 10 reference points for each reference line), and repeatedly executing the second step and the third step. And finally, obtaining a cross positioning point set after the false point pretreatment. For the subsequent cluster analysis false point removing method, the method can be directly operated on the cross positioning point set after the simplification pretreatment; for the data association false point removing method, two sight line vectors forming the false points cannot be associated and combined together, and the data association combination number is obviously reduced.
In the embodiment, a matlab tool is used for carrying out simulation verification on the false point removal preprocessing method based on the datum line pairwise crossing positioning point distance according to three observation stations and five target conditions.
The simulation conditions were as follows:
for simplicity, the following assumptions are made for this algorithm model:
1. all engineering errors are superposed into direction finding errors, and the direction finding precision of all observation stations is the same;
2. assuming that the target is stationary or moving at a very low speed;
3. the angle measurement errors follow Gaussian distribution with the mean value of zero, and the angle measurement errors of each observation station are independent;
4. to simplify the model, all stations and targets are in the XOY plane.
The parameters are set as follows:
the position coordinates of the three observation stations are respectively: (0,30), (0, -30), and (0, 0). The position coordinates of the five objects are (150,80), (155,80), (145,80), (150,85), and (150,75), respectively.
1. Taking 100 measurement data as primary simulation data, table 1 shows false point deletion rates when the observation station angle error delta is 0.05 °, delta is 0.15 °, delta is 0.25 °, and the error rejection rate parameter is set to be beta 0.01, beta 0.02, beta 0.03, beta 0.04, and beta 0.05, respectively.
Table 1:
2. taking 100 measurement data as primary simulation data, table 2 shows the true point deletion rates when the observation station angle error delta is 0.05 °, delta is 0.15 °, delta is 0.25 °, and the error rejection rate parameter is set to be beta 0.01, beta 0.02, beta 0.03, beta 0.04, and beta 0.05, respectively.
Table 2:
in summary, the following steps: the invention discloses a false point removal preprocessing method based on a distance between paired crossing positioning points of reference lines, and belongs to the field of electronic countermeasure. The method comprises the following steps: step one, selecting different sight vector samples of two different stations optionally, and giving a double-station cross positioning result. Traversing all the data association combinations to form a double-station cross positioning point set; step two, taking a certain sight vector of a certain station A as a datum line and taking a cross positioning point of the certain sight vector of another station B as a datum point, and calculating a paired cross positioning point set of a station C (any one third station except A, B stations) corresponding to the datum line; judging whether the reference point is a false point or not by using the distance between the paired cross positioning points, and if so, removing the reference point from the set of the double-station cross positioning points; traversing the reference points corresponding to all the reference lines, and repeatedly executing the second step and the third step; and step five, the preprocessed double-station cross positioning points are aggregated and used for subsequent data association, so that the data association efficiency is improved, and the interference of false points is reduced. The invention utilizes the false point preprocessing method based on the distance of the datum line pairwise crossing positioning points to remove a large number of false points and reduce the computational complexity of subsequent data processing.
Claims (2)
1. A false point removal preprocessing method based on the distance between paired crossing positioning points of reference lines is characterized by comprising the following steps:
the method comprises the following steps: selecting different sight vector samples of two different sites, giving a double-site cross positioning result, traversing all data association combinations, and forming a double-site cross positioning point set;
step two: taking a certain sight line vector of a certain station A as a datum line, taking a cross locating point of the datum line and a certain sight line vector of another station B as a datum point, and calculating a paired cross locating point set of a station C corresponding to the datum line; site C is any one of the third sites except the A, B site;
step three: judging whether the reference point is a false point or not by using the distance of the paired crossed locating points, and if so, removing the reference point from the set of the two-station crossed locating points;
step four: traversing all the reference points corresponding to all the reference lines, and repeatedly executing the second step and the third step;
step five: the preprocessed double-station cross positioning points are aggregated and used for subsequent data association, so that the data association efficiency is improved, and the interference of false points is reduced;
the first step is specifically as follows:
a total of NS measurement stations are known, their coordinates being: (x)1,y1)、(x2,y2)、...、(xNS,yNS) Assume there are NT radiation source targets to measure site A (x)i,yi) And site B (x)j,yj) The direction-finding cross positioning is carried out on the nth radiation source,
suppose that the azimuth angles of the two measurement stations to the nth target are respectively thetaAn、θBnThen, according to the geometric relationship between the nth target and the two sites, the target coordinates can be estimated:
obtaining the estimated coordinates of the nth radiation source target
Traversing all the data association combinations to form a double-station cross positioning point set X;
the second step is specifically as follows: the intersection positioning point of a certain sight vector datum line of a certain station A and a certain sight vector of another station B is a reference point P, and the intersection positioning point of the sight vector of a station C and the datum line is PiNT, NT being the target number, (P, P)i) Called pairwise crossing anchor points, all (P, P)i) NT form a set of paired intersection anchor point sets;
if only one site is available except for the site A and the site B, one reference point corresponds to a set of paired crossed positioning point sets; if a plurality of sites are available besides the site A and the site B, one reference point corresponds to a plurality of pairs of cross positioning point sets, and each site except the site A, B and the reference point generate a pair of cross positioning point sets;
the third step is specifically as follows:
(1) if there are only three sites, each reference point only corresponds to a set of paired crossed anchor points: calculating the Euclidean distance between two points of each paired crossed positioning point in the paired crossed positioning point set; finding out the pairwise cross positioning point with the minimum distance to obtain the minimum Euclidean distance dmin(ii) a Calculating an azimuth angle value of a connecting line of the reference point and the third station, and adding two azimuth angle values corresponding to two sight line vectors forming the reference point to obtain three azimuth angle values; calculating to obtain a distance threshold value d according to the three azimuth angle values and the set false point false rejection rate betath(ii) a When d isminGreater than a distance threshold dthIf so, the reference point P is considered as a false point, and is deleted; otherwise, the point is a real point;
(2) if more than three sites exist, each reference point corresponds to a plurality of groups of paired crossed positioning point sets, each group of paired crossed positioning point sets has a minimum Euclidean distance, and as long as the minimum Euclidean distance corresponding to one group of paired crossed positioning point sets is greater than a distance threshold dthIf the reference point P is a false point, deleting the reference point P; otherwise, the data is retained.
2. The fiducial-line based paired cross-positioning of claim 1The method for preprocessing the false point removal of the point distance is characterized in that the distance threshold value dthThe calculation method of (2) is as follows:
a. let P and P' form a pair of crossed positioning points, and the crossed positioning points are formed by correctly associated sight line vectors, and the reference point P is an azimuth angle thetaAAnd azimuth angle thetaBThe determined estimated point, P', is determined by the azimuth angle thetaAAnd azimuth angle thetaCIs determined where thetaA、θB、θCAzimuth observations corresponding to the same target for sites A, B, C, respectively;
b. the coordinates of the point P and the point P' are represented by thetaA、θB、θCDetermining according to a cross positioning equation; calculating the distance function d between the point P and the point P' according to the coordinatesAB_ACDistance function with argument as azimuth observation: dAB_AC＝f(θA,θB,θC)；
c. F (theta)A,θB,θC) First order Taylor expansion is performed at three azimuthal values, approximated as
d. Is calculated to obtain
Mean μ and variance σ of2Wherein the azimuth angle theta is assumedA、θB、θCObey Gaussian distribution, variance, respectively
The method comprises the following steps of (1) knowing;
e. setting false point error rejection rate beta, i.e.
Satisfies the following conditions:
by finding the following independent variable as distance variable dSolving an equation:
where erf (x) is a function of the error,
solution of the equation, i.e. the distance threshold dth。
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