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H&ES RESEARCH, 2-2017 ПУБЛИКАЦИИ НА АНГЛИЙСКОМ ЯЗЫКЕ
AUTONOMOUS DEFINITION OF REFERENCE AZIMUTHS WITH USE OF THE EQUIPMENT OF CONSUMERS OF SPACE NAVIGATION SYSTEMS
Chernov Ivan Vladimirovich,
postgraduate student, Military Space Academy, St. Petersburg, Russia, 4ern86@bk.ru
ABSTRACT
Among in geodesic devices in family of high-precision gyrotheodolites (gyrocompasses) there were devices allowing to make definition of astronomical azimuths with the standard deviation (SD) 1-1,5". Values of the astronomical azimuths defined from standard deviation exceeding accuracy the devices by 3-5" [1] are necessary for calibration of such devices that is with standard deviation it is not worse 0,5".
At the heart of creation and periodical control's of bases of calibration of gyrotheodolites (gyrocompasses) lies the astronomical method of definition of an azimuth. The essence of this method consists in the determination of the azimuth of the stellar body and the simultaneous measurement of a horizontal angle between the sun and the local subject. For high-precision definition of an astronomical azimuth, the way through the sentinel sentry of the Polaris star is usually used. The program of definition of an azimuth with an accuracy of 1" has to be carried out this way within not less than two evenings and must consist of 18 receptions in direct and 18 receptions in the opposite direction. Besides for calcula-tion of the azimuths defined with SD 1" value of astronomical latitudes have to be known no more than with a mistake 3". Definition of a personal instrumental difference of observers is also necessary.To receive an astronomical azimuth with SD 0,5" it is necessary to make the observations consisting of several programs of definition of an azimuth with SD 1" different theodolites (the corresponding accuracy), different observers. Thus, the astronomical method of high-precision determination of coordinates and azimuths is rather composite in realization and demands the considerable time and strongly depends on weather conditions that can be critical at problem solving of geodetic support. As can be seen in addition to the complexity, the astronomical method does not provide required accuracy for to create bases of calibration modern gyrotheodolite.
Currently in solving problems topogeodetic and navigation software is widely used satellite equipment receiving signals from GLONASS and NAVSTAR systems. This article examines the possibility of using such equipmentfor expeditious creating of polygons for calibration modern means of autonomous orientation (gyrotheodolite, gyrocompass).
Keywords: the azimuth; autonomous orientation; high-precision orientation; operative orientation; gyrotheodolite; gyrocompass.
For citation: Chernov I. V. Autonomous definition of reference azimuths with use of the equipment of consumers of space navigation systems. H&ES Research. 2017. Vol. 9. No. 2. Pp. 54-58. (In Russian)
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Calculation of length of the orientable direction for achievement of the required accuracy of orientation
The idea of a method of definition of an azimuth with use of the equipment of consumers of space navigation systems (EK SNS) consists in the solution of the inverse geodetic task of a difference of coordinates of points received by the relative method of space geodesy.
At realization of the relative method of space geodesy are performed synchronous measurements of pseudo-ranges to observed satellites not less than on two points. From the received data are calculated the difference between the spatial rectangular coordinates AX, AY, AZ these points, which are then considered to be the measured values. The differences of coordinates turn out in common terrestrial coordinate system.
To calculate geodetic azimuths, on coordinates of point B, L, № with the measured differences of coordinates AX, AY, AZ calculates coordinates, B, T other points wich fix the these directions. And only now from the solution of the inverse geodetic task (IGT) of the received coordinates of points geodetic azimuths of the directions are calculated. For finding of a geodetic azimuth pass from a space geocentric conception of systems coordinates to topocentric horizontal system Y, X, Z'. Then the geodetic azimuth of A can be calculated from the equation
After apparent simplifications we will receive
( AY ' A = arctg -
I AX '
(1)
2 2 mAP
(6)
""A AX2 + AY2 In a denominator of this equation a square of length of the orientable direction D specified on the horizon plane. Therefore,
mAP D
(7)
Considering that accuracy of definition of increments of coordinates of the modern EK SNS makes about 2 mm+0,5 mm*D-km and using a formula (7), perhaps a priori to calculate SD of definition of a geodetic azimuth depending on length of the orientable direction. Results of calculation saregivenin fig. 1.
where AT, AX' — increments in a topocentric horizont system coordinates.
Let's assume that arguments of a formula (1) are independent. Then, using the equation of an standard deviation of function of independent arguments [2], we will receive expression of SD of calculation of an azimuth
Fig. 1. The expected SD ofdefinition ofgeodetic azimuths depending on the distance D between points installations ofEK SNS antennas given on the horizon plane
The analysis of the received results allows to draw a conclusion that application of the relative method of space geodesy without use of reference points (a land initial geodetic basis) allows to define geodetic azimuths with CD 0,5-0,3" with a length of orientable direction about 1000-2000 m. Now we will consider a problem of the choice of the orientable directions.
dA dAX
2 2 mAX P
dA dAY
2 2 mAY P >
(2)
where m. — SD of definition of an azimuth; mA „ mA „— SD of
A ' AX AY
definition of increments of coordinates; p - the number of seconds in a radian (206265). Let's find partial derivatives of this equation
-AY
dA
dAX AX2 + AY2
(3)
dA
AX
-AY
AX2+AY2
max p2 +
AX
AX2 +AY2
mAY P2 (4)
(AX2 + AY2 )
The choice of an azimuth of the orientable direction for achievement of the required accuracy
To increase accuracy and efficiency of the considered method, we will accept a hypothesis of equal influence in the same instant of various sources of mistakes on observed datas for any receiver in the local area (10-30 km) [4]. Then generally, when the zenith distance of the orientable direction will not be equal 90°, there will be a dependence of an error of orientation 8'A the directions from errors of definition of geodetic coordinates AB and AL. This dependence is described by the equation [1]
dAY AX2 +AY2
After substitution of partial derivatives in an assumption formula we will receive:
8A = (AB sin A -AL cos A cos B ) ctg z
(8)
Let SD of definition of increments on abscissa axes and ordinates be equal to mA, then the equation (4) will take a form
2 2 2 AX2+AY2
mA = mAP -—:-— (5)
where z — zenith distance of the orientable direction; B,L— the geodetic width and longitude of point from which the azimuth is defined.
From (8) it is visible what 8A also depends on an azimuth, a slope angle of the orientable direction and width.rom a formula (8) it is visible that even at errors, in the linear measure of the reaching 15 m, the difference (8A) between any azimuths from a set of the received vectors, will not exceed 0,1" at slope angles of the orientable direction less than 5 Besides, at the latitude of Moscow at orientation of the direction, the close to
m, -
A
2
2
2
m, =
2
2
2
m, =
rc/3 + nn, size 84=0. For definition of a condition of the choice of the direction at the arbitrariest width we will equate expression (8) to zero
AB sin A-AL cos A cos B = 0 (9)
having accepted AB = AL we will receive
sin A = cos A cos B (10)
Let's divide both parts of equality into cos4
A = arctg (cos B ) + nn (11)
The received expression is a direction choice rule at the arbitrariest width when determining azimuths of the directions with application of EK SNS without use of an initial geodetic basis under a condition AB = AL. In a case AB ± AL expression (11) will take a form.
A = arctg | | Icos B \ + nn
(12)
Let by means of EK SNS coordinates with an accuracy of 0,1m will be received. Having accepted a confidence interval 2,5 m we will receive that with probability 0,98 [2] ALe [-0,25, 0,25], ABe [-0,25, 0,25].
In this case maxAL/AB ^-t» that will not allow to define a direction choice rule at the arbitrariest width when determining azimuths of the directions with application of EK SNS without use of an initial geodetic basis. Then, having brought in AL and AB equal mistakes which considerably (much) will exceed values AL and AB, we will receive ALe [-0,25, 0,25], ABe [-0,25, 0,25]. In this case maxAL/AB =1,05. Results of calculations for a formula (11) and (12) are given in the fig. 2.
50 45 40 35 30
:25 ' го
15 10 5 0
-A= arctg(cosB)
—a
85
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
Fig. 2. Results ofcalculation ofazimuths zero SA for a slope angle ofthe orientable direction equal 5°
From results of calculation of azimuths zero 8A (fig. 2) can draw a conclusion that for an exception of azimuthal distortions at independent definition of a high-precision azimuth with application of EK SNS it is necessary to design geodetic network proceeding from the rule (11).
Thus, in case of high-precision orientation and excess of a slope angle of the orientable direction at a size of5° and more (orientation in the mountain area) needs to be considered 84. When using of the offered orientation method the account 84
is impossible as the geodetic basis necessary for calculation of sizes AB and AL geodetic coordinates is not used. However there is an opportunity to compensate 84 by the choice of the direction of the close to 4 = arctg(cosB) + nn. In this case the orientable direction will be almost completely saved from influence of systematic errors of orientation, the bound to lack of an initial geodetic basis. Further from this direction in the way "in all combinations" or the directions in the way of "circular receptions" the geodetic azimuth can be transferred by a goni-ometry method with initial to any direction.
Calculation of time of observations by the equipment of consumers of space navigation systems for achievement of the required accuracy of positioning and orientation
Phase ambiguities are allowed for obtaining coordinates at development of geodetic networks by the relative method of space geodesy. A disambiguation is called definition of the complete number of cycles bearing (lengths of waves) between the antenna and the satellite (searching of the whole value of number of lengths of waves).For measurements in the mode this whole value decides on post-processing (PP) which is used for definition of location with an accuracy at the level of centimeter during computerizing. For measurements in real time which are used for definition of location with an accuracy at the level of centimeter this whole value is defined during the process called by initialization. The resolving time of phase ambiguities of t0 for the modern satellite geodetic receivers (EK SNS) from 5 seconds tolO minutes [5].
After permission of phase ambiguities of EK SNS receives the solution of a navigation task (a phase method) with an interval of one second and more (intervals turn out less than 1 second by interpolation between one-second observations).
Accuracy of obtaining coordinates (SD) in the absolute mode of positioning for EK SNS deviation 5 m [5] today. This deviation is caused by the equivalent bias of pseudo-range (UERE) and a steric geometrical factor (PDOP) ^.Considering above described, it is possible to write down Ri = [X, Y, Z]+Ai = [X, Y, Z.] where A =f (UERE, PDOP);X, Y,Z — coordinates of the EK SNS installation;X, Y, Z. — the coordinates
7 V V I
of the EK SNS installation received during an era of ie [1,^], - the number of measurements (eras).
The true deviation A will include 0 casual and 8 a systematic component. Let the provision of EK SNS concerning Earth be constant, and the size 8 can be neglected. Then, the unbiased deviation of calculation of average coordinates will be compensated. In case of the normal distribution law of a deviation 0 the expectation of the M random value of R coincides with its arithmetic average
- \R] M (R) = R = ^
N
(13)
Having accepted that SD of determination of coordinates in the absolute mode of positioning for EK SNS will deviation mR. = 9,8 m, we will receive SD of an arithmetic average R (13) on
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Fig. 3. The expected SD ofthe average coordinates received with application ofan absolute method ofpositioning
VN
(14)
Visualization of the given dependence is presented in fig. 3. Using dependence (14), it is not difficult to write down a formula of time spent for achievement of the given SD of determination of coordinates
T = t0 + tN, N =
f V
mRi
(15)
where T — time spent for achievement of the set SD of determination of coordinates, t — time of one solution of a navigation problem of t = t-t-1; tQ — a resolving time of phase ambiguities.
The least interval of the solution of a navigation problem of to deviations one second. Proceeding from a formula (15), time of observations for achievement of the required accuracy of determination of coordinates will make: 12 min. - 1 m; 17 min. - 0,5 m,3h- 0,5 m.
In the given calculations systematic components of definitions of pseudo-range (UERE) and systematic components of the deviations caused by a steric geometrical factor (PDOP) are not considered. For increase in accuracy of definitions in the specified conditions it is expedient to apply PPP (Precise Point Positioning) to post-processing.
As so with accumulation of number of measurements coordinates of points are specified, also their differences will be specified, i.e. increments of coordinates, application of averaging of coordinates and increments allows to solve a problem of a high-precision binding of the fixed object on a daily interval of observations and to solve a problem of high-precision definition of an azimuth without use of an initial land geodetic basis, i.e. is autonomously.
Technique of use of the equipment of consumers of space navigation systems for independent definition of reference azimuths
Based on explained above it is possible to present a technique of application of EK SNS for independent definition of azimuths with the required accuracy.
The first step of a technique — "Calculation of length of the orientable direction for achievement of the required accura-
cy of orientation". Knowing the required SD of definition of an azimuth mA and accuracy of definition of increments of coordinates of mA, the distance (the basic line) on which is calculated by a formula (7) it is necessary to carry EK SNS antennas.
The following step — "The choice of an azimuth of the orientable direction for decrease in influence of an deviation of determination of coordinates". Knowing EK SNS installation site width, the azimuth with which the orientable direction has to coincide is calculated by a formula (11).
The third step is "Calculation of time of observations of EK SNS for achievement of the required accuracy of positioning and orientation". The formula (15) is used for calculations.
Observations with application of EK SNS are carried out according to the user's guide, but when keeping an indispensable condition — observations on points of the orientable direction have to be simultaneous.
Processing of observed datas is carried out in conclusion of a technique. Calculation of coordinates of point from which the azimuth according to an absolute method of positioning is defined is carried out. The received coordinates are used as initial for determination of coordinates by the relative method of space geodesy. The azimuth and zenith distance of the direction pay off with use of the received coordinates.
After the solution of IGT the zenith distance of z of the orientable direction is estimated. In case z exceeds 5 both coordinates of both points change at the equal size (which is much surpassing accuracy of obtaining coordinates) and IGT is solved once again. The second decision is made by total.
The offered technique will allow to apply EK SNS to independent definition of reference azimuths with the required accuracy, due to installation of rules of projection of situation on zenith distance, an azimuth and length of the reference direction, will also allow to define necessary time of observations.
References
1. Gusenitsa Y. N, Malakhov A. V Simulation model of reconfigurable metrological complexes functioning in the conditions of information uncertainty on the receipt of measurement funds for metrological service. Uchenye zapiski Kom-somolsk-na-Amure Gosudarstvennyy tekhnicheskiy universitet [Scholarly Notes of Komsomolsk-na-Amure State Technical University. Engineering and Natural Sciences], 2016. No. 111-1(27). Pp. 32-46. (In Russian).
2. Rusyaeva E.A. Teoriya matematicheskoj obrabotki geo-dezicheskih izmerenij. CHast' 1. Teoriya oshibok izmerenij [The theory of mathematical processing of geodetic measurements. Part 1. Theory of measurement errors], Moscow: Mosk-ovskiy gosudarstvennyy universitet geodezii i kartografii Publ., 2016. 56 p. (In Russian)
3. Antonovich KM. Ispolzovanie sputnikovyx radion-avigacionnyx sistem v geodezii [The use of satellite navigation systems in geodesy]. In 2 vol. Moscow, Kartgeotsentr, 2006. 360 p. (In Russian)
4. Astapovich A. V, Bogachev A.N., Makarov S.A. Teoriya matematicheskoj obrabotki izmerenij. Part 2. Metod nai-
m
Ri
m
men'shih kvadratov [The theory of mathematical processing of measurements. Part 2: Method of least squares], St. Petersburg: Voenno-kosmicheskaya akademiya imeni A.F. Mozhayskogo-Publ.,2014. 102 p. (In Russian)
5. Precision of GLONASS/GPS navigation definitions. Russian system of differentional correction and monitoring. URL: http://www.sdcm.ru/smglo/ (date of access 16.01.2017). (In Russian)
АВТОНОМНОЕ ОПРЕДЕЛЕНИЕ ЭТАЛОННЫХ АЗИМУТОВ С ПРИМЕНЕНИЕМ АППАРАТУРЫ ПОТРЕБИТЕЛЕЙ КОСМИЧЕСКИХ НАВИГАЦИОННЫХ СИСТЕМ
Чернов Иван Владимирович,
адъюнкт Военно-космической академия имени А.Ф. Можайского, г. Санкт-Петербург, Россия, 4ern86@bk.ru
АННОТАЦИЯ
Среди геодезических приборов в семействе высокоточных гиротеодолитов (гирокомпасов) уже появились приборы позволяющие производить определение астрономических азимутов со средней квадратической ошибкой (СКО) 1-1,5". Для эталонирования таких приборов необходимы значения астрономических азимутов определённых со СКО превышающей точность эталонируемых приборов в 3-5 раз [1], то есть с СКО не хуже 0,5".
В основе создания и периодического контроля баз эталонирования гиротеодолитов(гирокомпасов) лежит астрономический метод определения азимута. Сущность этого метода состоит в определении азимута светила и одновременном измерении горизонтального угла между светилом и местным предметом. Для высокоточного определения астрономического азимута обычно используется способ по часовому углу Полярной звезды. Программа определения азимута этим способом с точностью 1" должна выполняться в течение не менее двух вечеров и состоять из 18 приёмов в прямом и 18 приёмов в обратном направлении. Кроме того для вычисления азимутов, определяемых с СКО 1", значение астрономических широт должны быть известны с ошибкой не более 3". Кроме того необходимо определение личной инструментальной разности наблюдателей. Для получения астрономического азимута с СКО 0,5" необходимо производить наблюдения состоящие из нескольких программ определения азимута с СКО 1" разными теодолитами (соответствующей точности), разными наблюдателями.
Таким образом, астрономический метод высокоточных определений координат и азимутов является достаточно сложным в реализации и требует значительного времени и сильно зависит от метеорологических условий, что может быть критичным при решении задач геодезического обеспечения. Как видно помимо трудоёмкости, астрономический метод не обеспечивает требуемые для создания баз эталонирования современных гиротеодолитов точности.
В настоящее время при решении задач топогеодезического и навигационного обеспечения широко используется спутниковая аппаратура (АП КНС), принимающая сигналы от навигационных систем ГЛОНАСС и 1\1ДУБТДР. В настоящей статье рассматривается вопрос о возможности применения такой аппаратуры при оперативном создании полигонов эталонирования современных средств автономного ориентирования (гиротеодолитов, гирокомпасов).
Ключевые слова: азимут; автономное ориентирование; высокоточное ориентирование; оперативное ориентирование; гиротеодолит; гирокомпас.
Для цитирования: Чернов И. В. Автономное определение эталонных азимутов с применением аппаратуры потребителей космических навигационных систем // Наукоемкие технологии в космических исследованиях Земли. 2017. Т. 9. № 2. С. 54-58.
