RU2645549C2 - Method of aircraft coordinates determining based on using two directional angles and one elevation angles - Google Patents

Abstract

FIELD: aviation; measurement technology.

SUBSTANCE: invention relates to an aircraft position determining method. To determine the aircraft position in a Cartesian coordinate system, marks are made from two measuring points with known coordinates of one direction angle and two elevations with subsequent processing of the received information on the computer. Determining the aircraft coordinates by solving the geometric problem of a straight circular cone intersection with a vertical axis of symmetry and the center in the second measuring point with a straight line passing through the first measuring point.

EFFECT: enabling increase in the accuracy of the aircraft coordinates determining and reducing the processing time of information when determining them.

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Description

The invention relates to the field of detection and determination of coordinates of aircraft and can be used in military equipment.

There are various methods for determining the coordinates of objects using methods for transmitting and receiving radio signals from ground-based radio beacons (RF patent No. 2436232) and a method of triangulating targets (RF patent No. 2423720) [1, 2]. The disadvantages of these methods is the difficulty of processing information from points of detection of objects, the use of only the active radar range of electromagnetic waves.

A method for automatically determining the coordinates of unmanned aerial vehicles (RF patent No. 2523446 - prototype) [3], consists in using circular cameras, a space-oriented video monitor, a computer and a laser range finder to illuminate the aircraft, characterized in that the circular cameras are located symmetrically and directed in different directions, so as to conduct 360 ° observation in the optical range of electromagnetic waves day and night, and the appearance of the aircraft is detected automatically as the xa that occurs on the frame of the video sequence relative to the previous one, and the obtained data are processed on a computer, where the angular values of the aircraft’s location are generated in the horizontal height relative to the center of the angle measuring device, which, using rotary mechanisms, directs the laser rangefinder to the aircraft to measure the distance to it, then the measured distance from the aircraft enters the information processing and display device (computer), where automatic ation determining spatial coordinates _{of UAV} X, Y _UAV, Z _UAV aircraft.

The main disadvantages are the unmasking component of this method associated with the use of laser radiation, which reduces the efficiency of using the above method for detecting and determining the spatial coordinates of aircraft in a hidden mode of operation, as well as large errors of the rotary mechanisms in the process of aiming the laser rangefinder and processing the received information.

As a common drawback of these methods for determining the coordinates of aircraft is not the full use of measurement data and, as a consequence, not the maximum accuracy.

The challenge facing the present invention is to increase the accuracy of determining the coordinates of aircraft and reduce the time it takes to process the received information in passive and active modes of operation.

The problem is solved as follows.

At present, the direction-finding method for determining the coordinates of objects is widespread in the practice of optical and radar external trajectory measurements. It is based on measuring the angular coordinates of the object in the horizontal (azimuth or directional angle) and vertical (elevation angle) planes (Fig. 1). In this case, two measurement points (PI) are enough to uniquely determine the spatial coordinates of the aircraft.

As a result of measurements from two PIs, the values of the directional angles and elevation angles (α ₁ ; ε ₁ ) and (α ₂ ; ε ₂ ) are determined, according to which the coordinates of the object are recalculated in a rectangular geodetic coordinate system.

where B is the base, i.e. distance between FE;

And _X is the azimuth (directional angle) from one IP to another.

Further necessarily synchronous measurements of these angles allows you to calculate the coordinates of the object related to subsequent points in time.

But even in this case, it is noteworthy that the totality of the measured parameters, which are four numbers, contains a certain redundancy of data, since the minimum information necessary to determine the position of the center of mass of an object (aircraft) in any SC should contain three independent measurements. This is also evidenced by the fact that the number of degrees of freedom of a material point is three. This fact is confirmed by the form of the above dependencies, which as arguments contain only three quantities (A ₁ , A ₂ , ε ₁ ). Usually the fourth parameter is either completely discarded, or at best used for control. However, in either case, information is lost.

It is known from theory that a pair of numbers (α; ε) geometrically uniquely defines a line in space. With two measuring points of such lines, two can be built. These lines intersect at the point where the object is located at the time of notching. However, if there are measurement errors, the direct SP _i -O in the general case will not intersect at one point, but will be crossed. The true position of the object will be determined by a certain region of space, which will be the greater, the lower the accuracy of measurement of quantities (A _i , ε _i ). Improving the reliability of the results can be achieved by increasing the number of PIs, but in this case it is not possible to use the classical dependences (1). Thus, it is necessary to look for other ways of processing the results of the VTI.

The minimum information necessary to determine the position of the center of mass of an object (aircraft) in any SC should contain three independent measurements.

In the future, the problem is reduced to recalculating the three initial values of the spherical SC into the three of the desired values of the rectangular SC. The number of possible combinations of triples of numbers from four is equal to C ³ ₄ = 4. Two fundamentally different geometric approaches to solving the problem of determining the object are possible here.

The initial data are the quantities (α ₁ ; ε ₁ ; ε ₂ ) or (ε ₁ ; α ₂ ; ε ₂ ). The first two of them (α ₁ ; ε ₁ ) also determine the line passing through IP ₁ in the direction of the object. The locus of points for which ε ₂ = const is a straight circular cone with a vertical axis of symmetry and a vertex in FE ₂ . The position of the object in this case will be determined by the point of intersection of the line and the cone (Fig. 2).

A plane and a straight round cone in space can be located in one of the following images (take into account one of the two parts of the cone).

1. The line passes through the top of the cone and coincides with its generatrix. In this case, these objects will have an infinite number of common points.

2. The line passes through the top of the cone and does not coincide with its generatrix. In this case, the line and the cone have one common point - the vertex.

3. The line is parallel to the generatrix of the cone, lies outside it and does not pass through the vertex. In this case, these objects do not have common points.

4. The line is parallel to the generatrix of the cone, lies inside it and does not pass through the vertex. In this case, the line and the cone have one common point.

5. The straight line is not parallel to the generatrix of its cone and does not pass through the vertex. In this case, the line and the cone have either two common points, or there are no such points.

The fifth case is most often implemented in practice. In the case when there are two intersection points, it is necessary to introduce additional conditions for choosing one of them. As such, the condition of proximity to a true solution, determined at least approximately, can be used. In the case under consideration, it is advisable to use the solution obtained by the first method as the true value.

After receiving the four positions of the object, the final one can take the weighted average value, where it is advisable to take the values inverse to the squares of the median errors of measurement of these values as the weight. Calculation of them "manually" is impossible, therefore, as a first approximation, we can restrict ourselves to the arithmetic mean of four values.

The equation of a straight circular cone with a vertical axis of symmetry passing through PI ₂ (x ₂ ; h ₂ ; y ₂ ) has the form

,

,

where a is the radius of the section of the cone at a height c from the top.

From FIG. 2 it follows that tan ε ₂ = c / a, then c = a tan ε ₂ . With this in mind, we rewrite the cone equation in the form:

.

.

or

.

.

The equation of the line will have the form

Substituting the quantities x, h, y from the parametric equation of the line

x = x ₁ + kcosε ₁ cosα ₁ ; h = h ₁ + ksinε ₁ ; y = y ₁ + kcosε ₁ sinα ₁

in the cone equation, we get

Expanding in powers of k, we obtain

or simplifying

;

;

;

;

.

.

Thus, we obtained a quadratic equation for the parameter k, the solution of which has the form:

D = b ² -4ac; k _1,2 = (- b ± √ Д) / 2а.

The value of b is even, so the solution can be found through the _^fourth D.

D / 4 = (b / 2) ² -ac; k _{1, 2} = [- (b / 2) ± √ _^(1/4 D)] / a.

Determine the position of the object in the GSK

x _G = x ₁ + kcosε ₁ cosα ₁ ; y _G = y ₁ + ksinε ₁ cosα ₁ ; y _Г = y ₁ + kcosε ₁ sinα ₁ .

Thus, the method of determining the spatial coordinates of aircraft based on the use of one directional angle and two elevation angles, which allows determining the position of the aircraft, in this case, will be determined by the point of intersection of the straight line and the cone, which reduces the processing time of the received information from sensors operating in optical and radar ranges of electromagnetic waves.

Information sources

1. Panov V.P., Prikhodko V.V. A method of transmitting and receiving radio signals of ground beacons. - FIPS. Patent for invention No. 2436232, 12/10/2011

2. Bezyaev B.C. A way to triangulate goals. - FIPS. Patent for invention №2423720, July 10, 2011

3. Shishkov S.V. A method for automatically determining the coordinates of unmanned aerial vehicles. - FIPS. Patent for invention No. 2523446, 05/26/2014

Claims (5)

A method for determining the position of an aircraft in a Cartesian coordinate system based on a notch from two measuring points with coordinates (x ₁ , h ₁ , y ₁ ) and (x ₂ , h ₂ , y ₂ ) of one directional angle α ₁ and two elevation angles ε ₁ , ε ₂ with subsequent processing of external path information on a computer by solving the geometric problem of intersecting a straight circular cone with a vertical axis of symmetry and a center in the second measuring point with a straight line passing through the first measuring point, algebraically reduced to finding the roots of the quadratic equation of the form with respect to the parameter k of the form k ² [cos ² ε ₁ tg ² ε ₂ -sin ² ε ₁ ] + k [2cos ε ₁ cos α ₁ (x ₁ -x ₂ ) tg ² ε ₂ + 2cos ε ₁ sin α ₁ (y ₁ -y ₂ ) tg ² ε ₂ - 2sin ε ₁ (h ₁ -h ₂ ) + (x ₁ -x ₂ ) ² tg ² ε ₂ + (y ₁ -y ₂ ) ² tg ² ε ₂ - (h ₁ -h ₂ ) ² = 0, and the subsequent determination of the desired coordinates of the aircraft (x _G , h _G , y _G ) according to the dependencies of the form: x _G = x ₁ + k cosε ₁ cos α ₁ ; h _G = h ₁ + k sin ε ₁ ; at _Г = y ₁ + k cos ε ₁ sin α _1.

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