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8TECHNICAL SCIENCES
METHOD OF COMPENSATION OF THE INFLUENCE OF THE VERTICAL COMPONENT OF THE CARRIER SPEED VECTOR IN RADAR METER OF MOTION PARAMETERS WITH TRANSCEIVER MODULE OF TWO-ANTENNY (JANUS) TYPE
Bakhmat M.,
Doctoral Student
Hetman Petro Sahaidachnyi National Army Academy, Lviv, Ukraine ORCID ID: https://orcid.org/0000-0002-4947-0762
Budaretskiy Yu.,
Candidate of Technical Sciences, Senior Researcher Hetman Petro Sahaidachnyi National Army Academy, Lviv, Ukraine ORCID ID: https://orcid. org/0000-0002-8882-03 74
Hrabchak V.,
Doctor of Technical Sciences, Senior Researcher Hetman Petro Sahaidachnyi National Army Academy, Lviv, Ukraine ORCID ID: https://orcid.org/0000-0003-3569-0681
Kazan P.,
Candidate of Military Sciences Hetman Petro Sahaidachnyi National Army Academy, Lviv, Ukraine ORCID ID: https://orcid.org/0000-0001-5929-0469.
Maneliyk A.
Teacher
Hetman Petro Sahaidachnyi National Army Academy, Lviv, Ukraine ORCID ID: https://orcid.org/0000-0001-6213-7182
Abstract
A technique is proposed to estimate errors in determining the speed and the distance passed by ground mobile objects using the radio locating instrument of movement measuring, which considers the vertical component of the velocity vector of the object due to vertical oscillations of its body and reduces errors in estimating motion parameters conditioned by it during movement through rugged country.
Keywords: navigation system, survey defects, Doppler meters, radio locating instrument of movement measuring.
Introduction
Navigation information is information about the coordinates of objects, the value of their speed, acceleration, course, roll, and tangage in a single dimension of time. The value of coordinates, speed, angles of course, roll, and tangage received the denomination of navigation system or navigation information. The availability of high-tech navigation information on board of ground mobile objects (GMO) allows to secure drafts navigation, topographic and geodetic survey of objects, and also can help to solve problems of automated management of unit's machines, which was impossible before [1-3]. Therefore, obtaining reliable navigation information is an urgent problem.
From the theory of the construction of Doppler meters, it is known that the greatest influence on the result of measuring horizontal components of the speed of the NRA when moving through rugged country has a common effect of roll and tangage [4-6].
During the hitting on obstacle, except the roll, there is a vertical movement of the GMO in relation to the earth's surface. This movement occurs due to the elasticity of the suspension system of the chassis (torsions, springs, etc.) [7].
Determining the vertical component of the GMO velocity vector and accounting for the error conditioned
by it increases the accuracy of determining the horizontal component of the GMO velocity vector.
With an aim to determine the error's dependence of the horizontal component of the velocity vector on the vertical component, make the following assumptions:
- an orientation of transceiver module's (TM) radar meter of motion parameters (RMMP) antennas rays is transverse diametral (Janus type), chart orientation of which arranged at an angle of 90° to each other and at an angle of 45° to the road and directed back-forth relative to the direction of movement;
- In RMMP are used frequency-independent combined by receiving and transmitting antennas in the Doppler sense;
- the signal propagation time is less than a quarter of the period of oscillation;
- Information about the angles of inclination from external sensors is entered into the RMMP equipment.
During the movement of the object on which the RMMP is installed, relative to the irradiated by its PPM surface, the values of the Doppler frequency ffl and the radial velocity Vr are related by a known expression [8]:
f = -c
(1)
where fd [Hz] Doppler frequency of shift, fd = fdi -fà2, fdi, fd2 - Doppler frequency according to the rays in the direction forward and backward relative GMO (pic. 1);
Vr [m/s] - radial component of the speed of mutual movement of objects;
f0 [Hz] - carrier frequency of the probing signal;
c=3x108 [m/s] - the velocity of spreading of radio waves.
The value Vr is related to the movement speed of the installation object relative to the irradiated surface Vx like
Vr = Vx • rnsy
(2)
where y - the angle between the velocity vector of the object on which the RMMP is installed, and the direction or the irradiated surface:
Picture 1 - Scheme of probing the earth's surface
In real conditions, the true values of Doppler frequency along the longitudinal rays of the directional characteristics can be described by the expressions:
f.
d1
f
d2
= 2fo_
c
JJjl
c
V.
V.
cos (r + ïi ) + Vz • cos (r-ïi ) + VZ
sin
m (r + ïi )], m (r-ïi )]
sin
(3)
(4)
where is an vertical component of the velocity vector; Yi - the current value of the tangage's pitching angle.
The vertical component of the velocity (pic. 1) leads to the dispersion of the irradiation angle y, which causes the error in estimating the velocity and the distance in its presence.
In this case, the measurement error of the longitudinal horizontal component of the velocity vector, if no special compensation measures are taken, according to [4, 9, 10] will have the following dependence:
2
w AVX r2 +VZ . 8VX = —x = — ± — • simr.
Vx 2 Vx 1
(5)
From (5), it is seen that in the presence of Vz and in the absence of Vx, the Janus system allows one to effectively compensate for the influence of Vz (Vz is equal to 0). However, in the presence of Vx or static slopes, compensation of Vz does not occur [9].
Picture 2 - three-dimensional scheme ofprobing the earth's surface TR, where fi - the angle of turn, p - of the
roll, 9 - of the tangage
In pictures 3-4 we show the graphical dependences of the error VX, calculated by (5).
-1 -0,5 -0 0,5 1
Picture 3 - Graphical dependence of SVXfrom VZ/VX
Picture 4 - Graphical dependence of SVx eld Vx
The sense of a method proposed to compensate for the influence of Vz, is that summarizing by taking into account the correction for the angular position, of the Doppler frequency on opposite rays of the corresponding coordinate allows obtaining information about Vz with some accuracy.
After summarizing (3) and (4) and simplifying, we come to the following:
4Vx • f0 . . 4Vz • f0 . FAXYj = —x ' smY 'smYi H--z • sin/- cosYi . (6)
After simple conversions (6) we obtain:
c • F,
ffx z
■ + Vx '
sinYi
4 fo • sin y • cos Yi " cos yi
Taking (3) and (4) into account, the expression for the difference in frequency will have the form.
F
ffXA
_4Vx • fo
• cos y • cos Yi ■+
4VZ- fo
• sin y • cos Yi.
(7)
(8)
C C
After solving (8) concerning VX, taking into account (7), and conversion, we obtain the following expression:
1
r
\
VxDaCH ---FPXA ■ cosrt —:--Fffxs ■ smYt . (9)
p 4f0 ycosy siny^ )
Determining the velocity by formula (9) can significantly reduce the effect of Vz on the measurement result of the velocity vector and reduce its error.
The error in determining Vx for the considered algorithm will be determined mainly by the discrepancy of the ratio c/siny with the true current value of the speed of light and the angle of the beam of the antenna diagram. The error formed by the application of formula (9) is defined as:
AVv
SVx =
' pacn
VV
Vx Vx
pacn
V
V
1.
(12)
Taking into account (6), (7), (10), after substitution and conversion, expression (10) will take the form:
Convert
Vr = V- i COS Y2 + — • sin Yj • COS Yj
x pam x | ' i V
/
/
arccos
\\
— • COSYo v Co yj
sinYo 2 V
-sinyi + — • cosYi • sin/i Vx
K = ^ • sin c
arccos
• cosYo
v co
then after the conversion, we get
SVx = sm/ifl - K)
V
V-
co_
c
J J
• cos/i - sin/i
(13)
(14)
(15)
The use of the involved technique allows us to detect and recover errors for account of Vz and increase the accuracy of determining navigation parameters.
Conclusions:
A technique has been developed to reduce the error in determining the speed and distance passed by GMOs using RMMP by taking into account the vertical component of the GMO velocity vector.
It is shown that for GMOs moving at low speeds, there is a need to take into account the error value due to the vertical component of the velocity vector.
The proposed technique can be used by developers of military equipment with the aim to create software for obtaining navigation information with high accuracy.
References
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