RU2078309C1 - Method of determination of space coordinates of target - Google Patents

Abstract

FIELD: proving ground tests of samples of armament and military equipment. SUBSTANCE: for determination of space coordinates of target n reference points are chosen, targets and reference points are sighted and photographed from N points with known coordinates, photographs are interpreted, reference points are identified, coordinates of reference points are measured in coordinate system which two axes lie in plane of photograph and third one is perpendicular to this plane and passes through center of photograph and space coordinates of target are calculated by coordinates of reference points known a priori and by measured coordinates of same reference points. For increase of accuracy of determination of coordinates direction cosines are additionally measured for each observation point between sighting lines to reference points and between directions passing through rear main point of photoregister and images of reference points, they are intercompared and direction cosines measured between directions passing through rear main point of photoregister and images of target and reference points are compensated by value of obtained difference, then space coordinates of object are determined by compensated values of direction cosines and known directions to reference points as point of crossing of right circular cones with vertex of each of them coinciding with observation point ands semispan of angle is equal to angle between directions to target and reference point. EFFECT: increased accuracy of determination of space coordinates of target.

Description

 The invention relates to field tests of samples of weapons and military equipment and can be used to determine the motion parameters of the objects of observation / testing / according to photo-recording / optical / means of trajectory measurements.

 The so-called direction-finding method is known for determining the spatial coordinates of a target from optical measurements from two or more points spaced in space. The position of the target in space in this case is defined as the intersection point of the n-lines of sight, where n is the number of optical means involved in the measurements. Moreover, each line of sight in space is determined by the azimuth (α) and elevation angle (β) (α, β are the angular coordinates of the target).

 To measure the angular coordinates of the target, each optical device is horizontal and the internal reference system is oriented relative to the local meridian and horizon, using, for example, geodetic milestones. In other words, they form high-precision orientation systems / reference coordinate systems / relative to the axes of the local measuring coordinate systems / SK / with the beginning at the main point of the lens of each optical means. The accuracy of the measured angular coordinates of the target largely depends on the accuracy of the estimates of the position of the reference SK relative to the axes of the measuring coordinate system. In addition, it is also necessary to know with sufficient accuracy a number of other orientation elements for each image: the focal length of the camera, the position of the optical center in the image, etc. As a result, the implementation of such measurements requires the preliminary implementation of complex adjustment, evaluation and geodetic works. The accuracy of the determined spatial coordinates of the target depends not only on the accuracy of angular measurements, but also on the number of optical devices and the geometry of their placement relative to the position of the target.

 These features make it difficult to widely use the direction finding method when organizing measurements, especially from temporary points in unequipped areas.

 The closest analogue to the invention is a method of observing an object against the background of reference points / 1 /. This method is based on photographing the target against the background of reference points (for example, stars) using an optical device such as a ballistic camera.

 The essence of this method is as follows. Before photographing, each optical device is horizontal and with the help of geodetic milestones it is oriented relative to the axes of the local measuring SC. According to the target designation, each optical device is aimed at the estimated area of the appearance of the object of observation. Photographing a target is performed, for example, against a background of stars. The obtained results of photographic registration after development are decrypted.

 The decryption results and the orientation data of the optical means relative to the axes of the local measuring SC are then used for identification / identification, recognition / stars of the image with the catalog. Further, using the picture and catalog coordinates of the identified stars, they refine the orientation elements of each image or determine their constants. As a result, the orientation parameters of each photo-recording medium turn out to be refined. After these operations, they proceed to calculate the angular coordinates of the target as a function of time / azimuth, elevation angle /.

 The output results of target photo-registration against the background of stars / reference points / from each optical means are two parameters: azimuth and target elevation angle. The determination of the spatial coordinates of the target can then be carried out, for example, in exactly the same way as in the direction finding method.

 The main disadvantage of this method is the dependence of both the process of identifying the stars of the image with the catalog and the accuracy of measuring the angular coordinates of the target on the accuracy and reliability of the estimates of the orientation parameters of each optical means relative to the axes of the measuring SC. Therefore, laborious adjustment and geodetic works are performed before measurements. These circumstances make it difficult to use this method in unequipped areas.

 In addition, the use of control points / stars / is aimed only at clarifying orientation elements / constants / image and therefore the output measurement results are the angular coordinates of the target at fixed points in time. At the same time, n reference points / stars / with high-precision coordinate values are excluded from the output information, which ultimately limits the possibility of increasing the accuracy of the determined spatial coordinates of the target due to, for example, redundancy of measurements from each optical means. On the other hand, it should be noted that the use of geodetic milestones / points with different azimuths but approximately the same elevation angle relative to the standing point of the optical tool / makes the application of the processing method discussed above due to the particular arrangement of these reference points.

 The objective of the invention is to increase the accuracy of determining the spatial coordinates of the target by increasing the amount of measurement information.

The specified technical result is achieved in that each optical means involved in the work is set arbitrarily relative to the axes of the measuring SC. Then, each optical means is guided roughly (with an accuracy of 5.10 ^o / relative to the local meridian and horizon at the estimated area of the target. Photographing the target is carried out against the background of reference points. Here, reference points are understood as points with known directions in space (for example, given by the azimuth and elevation angle) with respect to the local measuring SC combined with the standing point of the optical tool / star, geodesic pole /. Known areas will be referred to below as catalogs.

 The obtained photo-registration materials with images of the target and reference points are developed and decrypted (including identification). Then, based on the coordinates of the control points / measured and catalog / determine the calibration parameters of each image. Calibration parameters are understood as characteristics allowing to take into account the distortion of the reference field due to negative deformation, lens distortion and aberration, difference between the actual focal length from the passport value, the displacement of the origin of coordinate systems, atmospheric refraction, etc. In this case, the orientation parameters / position of the optical axis relative to the axes of the measuring SK, the angle of rotation of the image / are not specified and are not used in the calculations.

 The obtained calibration parameters and the measured picture coordinates of the target and reference points are then used to obtain the guide cosines between the directions passing through the main rear point of the lens to the target image and the reference points of each picture. Thus, from each image, as many values of the guide cosines can be obtained as are accepted for processing control points.

 The spatial coordinates of the target are determined by the values of the guiding cosines and the known directions to the reference points as the intersection point, for example, of straight circular cones, the vertex of each of which coincides with the position of the optical means / main point of the lens /, and the half-angle is equal to the angle between the directions to the target and reference point.

 Consider the implementation of the method by the example of photographing a target against a background of stars.

где J количество оптических средств). Ось O_iY_i направлена, например, на север по касательной к истинному меридиану, проходящему через начало координат. Ось O_iY_i направлена по внешней нормали к эллипсоиду в точке O_i. Ось O_iZ_i образует с осями O_iX_i и O_iY_i правую прямоугольную систему координат. Как отмечалось выше, каждое оптическое средство совмещается с началом "своей" измерительной СК. Горизонтирование средств может не производиться. Наведение в предполагаемый район появления цели выполняется грубо с точностью до нескольких градусов /5.10^o/ относительно местных меридиана и горизонта. Указанная величина /5.10^o/ выбрана из тех предположений, что у баллистических камер угол поля зрения составляет, как правило, 20^o и более и потому объект наблюдения даже при такой погрешности ориентирования будет зафиксирован на снимке. Для подобного ориентирования оптического средства в пространстве может быть использован компас, топографическая карта, положение Полярной звезды и т.д. Необходимым условием является фотографирование цели на фоне звезд /т.е. одновременное фотографирование цели и опорных точек/.The position of the standing points of the optical means / the main points of the lenses / are determined by previously known geodetic methods. These points are the beginnings of local measuring coordinate systems O _i X _i Y _i

where J is the number of optical means). The axis O _i Y _{i is} directed, for example, to the north along the tangent to the true meridian passing through the origin. The axis O _i Y _{i is} directed along the external normal to the ellipsoid at the point O _i . The axis O _i Z _i forms with the axes O _i X _i and O _i Y _{i the} right rectangular coordinate system. As noted above, each optical device is combined with the beginning of its own measuring SC. Leveling of funds may not be made. Guidance to the intended area of the target’s appearance is carried out roughly with an accuracy of several degrees /5.10 ^o / relative to the local meridian and horizon. The indicated value of /5.10 ^o / was chosen from the assumptions that the angle of the field of view of ballistic cameras is, as a rule, 20 ^o or more, and therefore the object of observation, even with such an orientation error, will be fixed on the picture. For such an orientation of the optical means in space, a compass, a topographic map, the position of the North Star, etc. can be used. A prerequisite is photographing the target against the background of the stars / i.e. simultaneous photographing of the target and reference points.

 Suppose photographing is performed on a single frame. In this case, the trace of the target’s movement is recorded in the form of several tracks, each of which has a time reference. In the same way stars will be portrayed. The resulting negatives are then used to measure the coordinates of the images of the target and stars on a comparator, for example, type AK-1.

 The stars of a picture with a catalog are recognized either manually by star charts using negatives with the image of stars, or automatically using, for example, a special algorithm / cm. Yakushin S.M. A method of processing the results of photographing by optical means of space objects on the background of stars. Autometry, 1976, N 5, p. 58 62 /. As a result of identification, the catalog / visible / coordinates of the stars are determined. Using the catalog and picture coordinates of the stars, determine the calibration parameters of the image.

It is assumed that the negatives have a Gauthier grid and therefore corrections for the deformation of the photo material are calculated and introduced at the stage preceding the stage of evaluating the calibration parameters of each image. With this in mind, we include in the set of estimated parameters the characteristics that have the most significant effect on the accuracy of the measured cosines between the directions to the target and reference points. These characteristics are: the focal length of the camera / f /, the coordinates of the position of the optical center in the image / X ₀ , Y ₀ /, polynomial coefficients describing the effect of lens distortion / K ₁ , K ₂ , K ₃ /.

где X_ui, Y_ui измеренные значения картинных координат опорных точек.The initial dependencies for evaluating the calibration parameters in this case are:

where X _ui , Y _{ui are the} measured values of the picture coordinates of the control points.

To introduce corrections Δr for distortion at the distances measured from the main point in the image, a polynomial of the form
Δr = k ₁ λ ³ + k ₂ λ ⁵ + k ₃ λ ⁷
/cm. Lobanov AN Photogrammetry. M. Nedra, 1984, p. fifteen/.

частные производные от функции по соответствующей переменной;
Δf•Δx_o•Δy_o•Δk₁•Δk₂•Δk₃ поправки к начальным значениям оцениваемых параметров;
l cosQ_эт cosQ_расч;
cosQ_эт = cosβ₁•cosβ₂•cos(α₁- α₂)+sinβ₁sinβ₂
α₁,β₁,α₂,β₂ угловые координаты опорных точек.Applying the Taylor series, we write the equation of corrections

partial derivatives of a function with respect to the corresponding variable;
Δf • Δx _o • Δy _o • Δk ₁ • Δk ₂ • Δk ₃ corrections to the initial values of the estimated parameters;
l cosQ _et cosQ _calculation ;
cosQ _et = cosβ ₁ • cosβ ₂ • cos (α ₁ - α ₂ ) + sinβ ₁ sinβ ₂
α ₁ , β ₁ , α ₂ , β ₂ angular coordinates of reference points.

Значения частных производных определяются либо аналитически, либо методом конечных разностей.As the initial values are taken f _o f _n - passport value,

The values of the partial derivatives are determined either analytically or by the finite difference method.

 Each pair of control points allows you to create one equation with six unknowns. To evaluate the calibration parameters, you must have at least 4 reference points / a combination of 4 to 2 gives the number 6 /. In the general case, the number of equations / N / from n the number of reference points is determined by the expression / the number of combinations of n by 2 /.

Уравнения типа /4/ решаются последовательными приближениями, например, по методу наименьших квадратов.

Equations of the type / 4 / are solved by successive approximations, for example, by the least squares method.

 Having estimated the calibration parameters of each image in this way, then they proceed to determine the guiding cosines between the directions to the target and reference points. In this case, the values of the picture coordinates of each point / target, reference point / are corrected according to the rule / 3 /, after which the values for each pair / picture coordinates of the target and the next control point / according to the rule / 1 / are calculated.

где n число опорных точек, задействованных при оценке параметров калибровки;
α,β₁,...,α_n,β_n опорные направления в виде угловых координат /азимут, угол места/;
t момент времени.Having the correlation matrix of the estimated calibration parameters and the values of the measurement errors of the picture coordinates, we calculate the values of σ _cosQ which are then used to estimate the weight of the measured cosQ values. Next, an array of measured values of cosQ _i for a fixed point in time is formed for each image in the form:

where n is the number of reference points involved in the evaluation of calibration parameters;
α, β ₁ , ..., α _n , β _n reference directions in the form of angular coordinates / azimuth, elevation angle /;
t point in time.

 Arrays of the form / 6 / s of each optical means / image / at time t are the initial data for determining the spatial coordinates of the target. As noted above, the spatial coordinates of the target are defined as the intersection point of straight circular cones, the vertex of each of them coincides with the standing point of the optical means, and the half-solution angle is equal to the angle between the directions to the target and the reference point. Based on the foregoing, to determine the spatial coordinates of the target, as many values of the direction cosines are used as the total number of identified / recognized / stars with the catalog from all the images. In other words, if 3 optical means are involved in the work and 10 stars are recognized in each image, then in this method the coordinates of the target on t are determined by / 10x3 / cosQ values instead of 6 / 2x3 / α, β values, as, for example, in direction finding way. An increase in the amount of measurement information involved in processing allows one to increase both the accuracy and reliability of the determined coordinate estimates.

 The proposed method is based on an increase in measurement information, which ultimately leads to an increase in the accuracy of determining coordinate estimates with virtually no additional measurement costs. The method also provides the simplification of the actual measurements due to the refusal to build a high-precision orientation system for each optical device and thereby increase the flexibility and mobility of the measuring complex when solving the problem of estimating the target coordinates. Based on the proposed method, it is possible to create relatively cheap measuring optical systems with a coarse internal reference system / up to units of degrees / to ensure measurements in hard-to-reach and low-equipped areas.

Claims (1)

 A method for determining the spatial coordinates of a target, which consists in selecting n reference points, sighting and photo-recording of a target and reference points from N points with known coordinates, decrypting images, identifying reference points, measuring the coordinates of reference points in a coordinate system whose two axes lie in the plane of the photograph, and the third is perpendicular to this plane and passes through the center of the photograph, and calculates the spatial coordinates of the target using the a priori known coordinates of the control points and the measured coordinates of the same points, characterized in that the guide cosines for each observation point between the lines of sight at the reference points and between the directions passing through the rear main point of the photorecorder and the images of the reference points are additionally measured, they are compared with each other and the measured direction cosines between the directions passing through the rear main point of the photorecorder and the image of the target and reference points, and then determined by the compensated values of the direction constituents known cosine and directions to the reference point spatial coordinates of the object as the point of intersection of a right circular cone, the vertex of each of which coincides with the point of observation, and the half-cone angle equal to the angle between the directions of the target and the reference point.