CN102607560A - Two-station direction-finding cross positioning tracing algorithm on earth surface based on rhumb lines - Google Patents

Abstract

The invention designs an algorithm flow for carrying out cross positioning tracing by using rhumb lines of two observation stations on the earth surface. The invention provides a method for positioning and tracing a plurality of moving targets through crossing the rhumb lines by using two passive direction-finding sensors in a region which is at low latitude on the earth surface, so as to solve the problems of the traditional method that the adaptable region range is small, the positioning and tracing precision is low and the calculation amount is too great. The algorithm is characterized in that (1) in the algorithm principle, longitude and latitude coordinates of the two observation stations are positioned and the positions of a target relative to the two stations are respectively obtained by direction finding, so as to determine the rhumb lines which pass through each observation station from the measured azimuth angles; if the same target is observed, the two rhumb lines are crossed at one point and an approximate target position is obtained by revising a crossed point coordinate; (2) an algorithm formula derivation process is provided; and (3) the algorithm flow of intensive type cross positioning tracing and the algorithm flow of distribution type cross positioning tracing are provided based on the algorithm principle and the formula. The method disclosed by the invention is applicable to rapidly and accurately positioning and tracing of a plurality of moving targets, and has important applications values on aspects of military use and civil use.

Description

Earth surface is based on two station direction finding cross bearing track algorithms of loxodromic line

Affiliated technical field

The present invention is the method that the not high area of a kind of dimension at the earth's surface positions and follows the tracks of multiple mobile object through the loxodromic line intersection with two passive direction finding sensors.

Background technology

The extremely attention of Chinese scholars and relevant departments always of passive direction finding cross bearing and tracking technique owing to have advantage such as antijamming capability is strong, good concealment.The application of direction finding location technology is of long duration, and exactly the plane that is approximately in a certain zone, utilizes the method for plane geometry to carry out cross bearing calculating then, and not far when target range, this method was simple and effective when scope of activities was little.But continuous development along with technology; The continuous expansion of the scope of activities of the various land, sea and air vehicles; Movement velocity is more and more faster, and it is more and more obvious that the influence of earth curvature just becomes, and the error that this localization method causes has begun in application, to cause serious problems.

In theory in conversion through terrestrial coordinates and geocentric rectangular coordinate; Add the angle of pitch just can be in geocentric rectangular coordinate be the space localizing objects; Can convert terrestrial coordinates into then, thereby but realize cross bearing at too poor interception angle, two stations and the angle of pitch of can't in rectangular coordinate system, carrying out of the angle of pitch precision of the target that obtains through microwave, infrared radiation.

Make that the basic reason of utilizing the simple direction finding cross bearing in this once effective two stations to continue to play a role on the earth surface is to consider that the simple direction finding in two stations can only obtain two planes in the three dimensions of earth curvature from geometric meaning; And two planes have only and could obtain a line under the crossing situation, in any case but also can not get a point.Therefore must could realize the simple direction finding cross bearing in two stations by means of auxiliary calculating of other correlation properties of the earth itself.

Seeing that ship navigation sea area latitude is not high, when voyage is not far, calculate point of arrival coordinate or anti-error of separating course, voyage in order to reduce to paint, and when ship manoeuvre was frequent, loxodromic line boat method commonly used was carried out analytical Calculation, painted calculation to replace mapping.Go up at the earth's surface, loxodromic line generally shows as one and intersects spheric helix constant angle, that have dual curvature with all meridians, and it tends to the earth polar, but can not arrive the earth polar.Spend the loxodromic line of earth surface point with fixed angles and have only one.The acquisition ratio of considering the position of two research stations itself is easier to; And through the direction finding relative orientation of target of having got back, so just can be the loxodromic line of two research stations, if observation is same target; Then two loxodromic lines intersect at a point, the target location that obtains being similar to.

From domestic and international disclosed document, also find the correlative study report of the simple direction finding cross bearing in two stations of this method of application.

Summary of the invention

The present invention is on the basis of loxodromic line relevant knowledge in analyzing navigation, has designed practical earth surface and has followed the tracks of new algorithm based on two station direction finding cross bearings of loxodromic line, and concrete technology contents is:

Suppose that A and B are two direction finding platforms, C is a target, and the position angle that A records C is C _A, the position angle that B records C is C _B, position through A and C are with respect to the position angle C of A _ACan obtain loxodromic line l _AC, position through B and C are with respect to the position angle C of B _BCan obtain loxodromic line l _BC, at latitude not high (below 60 degree), under the situation of target relative height limited (1 myriametre is following), loxodromic line l _ACAnd l _BCIntersection point and the target C physical location of ordering be more or less the same, so we use loxodromic line l _ACAnd l _BCIntersection point suitably revise and represent C point coordinate value.Might as well establish l _ACAnd l _BCThe longitude and latitude of intersection point be (λ ₂, φ ₂), then with A (λ at this moment _A, φ _A) and B (λ _B, φ _B) satisfy loxodromic line system of equations (1) respectively.

$\left\{\begin{array}{c}{\mathrm{\λ}}_2-{\mathrm{\λ}}_A=\mathrm{tg}{C}_A\left\{\ln \right[\mathrm{tg}(\frac{\mathrm{\π}}{4}+\frac{{\mathrm{\φ}}_2}{2}){\left(\frac{1-e{\sin \mathrm{\φ}}_2}{1+e\sin {\mathrm{\φ}}_2}\right)}^{e/2}]-\ln [\mathrm{tg}(\frac{\mathrm{\π}}{4}+\frac{{\mathrm{\φ}}_A}{2})\left){\left(\frac{1-e\sin {\mathrm{\φ}}_A}{1+e\sin {\mathrm{\φ}}_A}\right)}^{e/2}\right]\}\\ {\mathrm{\λ}}_2-{\mathrm{\λ}}_B=\mathrm{tg}{C}_B\left\{\ln \right[\mathrm{tg}(\frac{\mathrm{\π}}{4}+\frac{{\mathrm{\φ}}_2}{2}){\left(\frac{1-e\sin {\mathrm{\φ}}_2}{1+e{\sin \mathrm{\φ}}_2}\right)}^{e/2}]-\ln [\mathrm{tg}(\frac{\mathrm{\π}}{4}+\frac{{\mathrm{\φ}}_B}{2}){\left(\frac{1-e\sin {\mathrm{\φ}}_B}{1+e\sin {\mathrm{\φ}}_B}\right)}^{e/2}\left]\right\}\end{array}\right.---\left(1\right)$

Get

$\left\{\begin{array}{c}{m}_A=\ln \left[\mathrm{tg}(\frac{\mathrm{\π}}{4}+\frac{{\mathrm{\φ}}_A}{2}){\left(\frac{1-e\sin {\mathrm{\φ}}_A}{1+e\sin {\mathrm{\φ}}_A}\right)}^{e/2}\right]\\ m_B=\ln \left[\mathrm{tg}(\frac{\mathrm{\π}}{4}+\frac{{\mathrm{\φ}}_B}{2}){\left(\frac{1-e\sin {\mathrm{\φ}}_B}{1+e\sin {\mathrm{\φ}}_B}\right)}^{e/2}\right]\end{array}\right.---\left(2\right)$

(2) substitution (1)

$\left\{\begin{array}{c}{\mathrm{\λ}}_2-{\mathrm{\λ}}_A=\mathrm{tg}{C}_A\left\{\ln \right[\mathrm{tg}(\frac{\mathrm{\π}}{4}+\frac{{\mathrm{\φ}}_2}{2}){\left(\frac{1-e\sin {\mathrm{\φ}}_2}{1+e\sin {\mathrm{\φ}}_2}\right)}^{e/2}]-m_A\}\\ {\mathrm{\λ}}_2-{\mathrm{\λ}}_B=\mathrm{tg}{C}_B\left\{\ln \right[\mathrm{tg}(\frac{\mathrm{\π}}{4}+\frac{{\mathrm{\φ}}_2}{2}){\left(\frac{1-e{\sin \mathrm{\φ}}_2}{1+e\sin {\mathrm{\φ}}_2}\right)}^{e/2}]-m_B\}\end{array}\right.---\left(3\right)$

Get

$m_{\mathrm{\φ}}=\ln \left[\mathrm{tg}(\frac{\mathrm{\π}}{4}+\frac{{\mathrm{\φ}}_2}{2}){\left(\frac{1-e\sin {\mathrm{\φ}}_2}{1+e{\sin \mathrm{\φ}}_2}\right)}^{e/2}\right]---\left(4\right)$

(4) substitution (3)

$\left\{\begin{array}{c}{\mathrm{\λ}}_2-{\mathrm{\λ}}_A=\mathrm{tg}{C}_A(m_{\mathrm{\φ}}-m_A)\\ {\mathrm{\λ}}_2-{\mathrm{\λ}}_B=\mathrm{tg}{C}_B(m_{\mathrm{\φ}}-m_B)\end{array}\right.---\left(5\right)$

Get by (5)

$\left\{\begin{array}{c}{m}_{\mathrm{\φ}}=\frac{{\mathrm{\λ}}_B-{\mathrm{\λ}}_A+m_B\mathrm{tg}{C}_A-m_B\mathrm{tg}{C}_B}{\mathrm{tg}{C}_A-\mathrm{tg}{C}_B}\\ {\mathrm{\λ}}_2=\mathrm{tg}{C}_A(m_{\mathrm{\φ}}-m_A)+{\mathrm{\λ}}_A\\ =\mathrm{tg}{C}_B(m_{\mathrm{\φ}}-m_B)+{\mathrm{\λ}}_B\end{array}\right.---\left(6\right)$

Get by (4)

$m_{\mathrm{\φ}}=\ln \left[\mathrm{tg}(\frac{\mathrm{\π}}{4}+\frac{{\mathrm{\φ}}_2}{2})\right]+\frac{e}{2}\ln \left(\frac{1-e\sin {\mathrm{\φ}}_2}{1+e\sin {\mathrm{\φ}}_2}\right)---\left(7\right)$

Get $\mathrm{\Δ}=\frac{e}{2}\ln \left(\frac{1-e\sin {\mathrm{\φ}}_2}{1+e\sin {\mathrm{\φ}}_2}\right)$

Get

${\mathrm{\φ}}_2=2\mathrm{antg}\left(e^{m_{\mathrm{\φ}}-\mathrm{\Δ}}\right)-\frac{\mathrm{\π}}{2}---\left(8\right)$

Through to (λ ₂, φ ₂) suitably revise the numerical value that just can draw the longitude and latitude of target C.This correction can realize through statistical law, also can realize through the further derivation of equation.

Description of drawings

Accompanying drawing 1 algorithm basic thought process flow diagram

Suppose that A and B are two direction finding platforms, C is a target, and the position angle that A records C is C _A, the position angle that B records C is C _B, position through A and C are with respect to the position angle C of A _ACan obtain loxodromic line l _AC, position through B and C are with respect to the position angle C of B _BCan obtain loxodromic line l _BC, at latitude not high (below 60 degree), under the situation of target relative height limited (1 myriametre is following), loxodromic line l _ACAnd l _BCIntersection point and the target C physical location of ordering be more or less the same, so we use loxodromic line l _ACAnd l _BCIntersection point suitably revise and represent C point coordinate value.

The algorithm flow that accompanying drawing 2 centralized cross bearings are followed the tracks of

1. measure the position of this research station, two faces of land;

2. these two research stations record the relative direction of target respectively;

3. the position of these two research stations and the relative direction that records target thereof are pooled to concentrator in real time with the network message form;

4. respectively with the position of each research station and record each observation station of direction calculating of target and the loxodromic line at target place;

5. the point of crossing coordinate that calculates two loxodromic lines of these two research stations of process and same target promptly obtains the position of target.

The algorithm flow that accompanying drawing 3 distributed cross bearings are followed the tracks of

1. measure the position of this research station, two faces of land;

2. these two research stations record the relative direction of target respectively;

3. separately the research station according to own position and record this point of direction calculating of target and the loxodromic line that target belongs to;

4. the loxodromic line parameter through each research station and target is pooled to concentrator in real time with the network message form;

The point of crossing coordinate correction of 5. calculating two loxodromic lines of these two research stations of process and same target promptly obtains the position of target afterwards.

Embodiment

The present invention has designed to utilize through the loxodromic line of two research stations, the face of land and has carried out two kinds of algorithm flows that cross bearing is followed the tracks of: the algorithm flow that algorithm flow that centralized cross bearing is followed the tracks of and distributed cross bearing are followed the tracks of.

(1) algorithm flow of centralized cross bearing tracking is shown in accompanying drawing 2:

1. measure the position of this research station, two faces of land;

2. these two research stations record the relative direction of target respectively;

3. the position of these two research stations and the relative direction that records target thereof are pooled to concentrator in real time with the network message form;

4. respectively with the position of each research station and record each observation station of direction calculating of target and the loxodromic line at target place;

5. the point of crossing coordinate that calculates two loxodromic lines of these two research stations of process and same target promptly obtains the position of target.

(2) algorithm flow of distributed cross bearing tracking is shown in accompanying drawing 3:

1. measure the position of this research station, two faces of land;

2. these two research stations record the relative direction of target respectively;

3. separately the research station according to own position and record this point of direction calculating of target and the loxodromic line that target belongs to;

4. the loxodromic line parameter through each research station and target is pooled to concentrator in real time with the network message form;

The point of crossing coordinate correction of 5. calculating two loxodromic lines of these two research stations of process and same target promptly obtains the position of target afterwards.

Claims (4)

1. the present invention has provided to utilize through the loxodromic line of two research stations, the face of land and has carried out algorithm thought and the derivation of equation process that cross bearing is followed the tracks of.Two kinds of algorithm flows have been designed: the algorithm flow that algorithm flow that centralized cross bearing is followed the tracks of and distributed cross bearing are followed the tracks of.

2. the general technical characteristic of algorithm thought and derivation of equation process:

The latitude and longitude coordinates of two research stations, location itself; Obtain the orientation at relative two stations of target respectively through direction finding; Definite loxodromic line of passing each research station with institute interception angle respectively; If observation is same target; Then two loxodromic lines intersect at a point, the target location that obtains being similar to after the intersecting point coordinate correction.

3. the technical characterictic of the algorithm flow that centralized cross bearing is followed the tracks of:

1. measure the position of this research station, two faces of land;

2. these two research stations record the relative direction of target respectively;

3. the position of these two research stations and the relative direction that records target thereof are pooled to concentrator in real time with the network message form;

4. respectively with the position of each research station and record each observation station of direction calculating of target and the loxodromic line at target place;

The point of crossing coordinate correction of 5. calculating two loxodromic lines of these two research stations of process and same target promptly obtains the position of target afterwards.

4. the technical characterictic of the algorithm flow that distributed cross bearing is followed the tracks of:

1. measure the position of this research station, two faces of land;

2. these two research stations record the relative direction of target respectively;

3. separately the research station according to own position and record this point of direction calculating of target and the loxodromic line that target belongs to;

4. the loxodromic line parameter through each research station and target is pooled to concentrator in real time with the network message form;

The point of crossing coordinate correction of 5. calculating two loxodromic lines of these two research stations of process and same target promptly obtains the position of target afterwards.

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