RU2516697C2 - Method of aircraft bank measurement and device to this end - Google Patents

Abstract

FIELD: aircraft engineering.

SUBSTANCE: proposed method consists in horizontal irradiation of linearly polarised electromagnetic waves from the points with known coordinates. Aircraft receives said electromagnetic waves in circular polarisation basis. Received electromagnetic waves are divided into two circularly orthogonal-polarisation components of the right and left rotating sense to measure phase difference there between. Measured phase difference is used to calculate aircraft bank.

EFFECT: ruled out accumulated errors.

2 cl, 2 dwg

Description

The invention relates to radio navigation and can be used in flight navigation systems for aircraft orientation (LA), for example, when approaching an aircraft for instrument landing.

Known methods and devices for measuring the roll angle of an aircraft are based on the use of inertial navigation systems, in particular gyroscopic orientation systems [1-4]. Such measurement methods and devices that implement them have a number of disadvantages. Firstly, over time, there is a constant accumulation of measurement errors and in one hour of flight it is a unit of degrees [2-3]. Secondly, if the aircraft develops significant overloads, then there is an increase in the gyroscope’s own precession rate, which in some cases can lead to a complete loss of its operability [2].

Since the known methods for measuring the roll angle of aircraft and devices that implement them are based on a different physical principle compared to the claimed one, they cannot be considered as analogues, since they do not have common features.

The essence of the proposed method for measuring the angle of heel of the aircraft is as follows.

From a point with known coordinates emit horizontally linearly

которых совпадает с горизонтальной плоскостью, и совместно с нормалью к этой плоскости образуют неподвижную декартовую прямоугольную систему прямоугольных координат.polarized electromagnetic waves, electric field vector $$\overrightarrow{E}$$

which coincides with the horizontal plane, and together with the normal to this plane form a fixed Cartesian rectangular system of rectangular coordinates.

и левого $${\overrightarrow{E}}_L$$

направления вращения вектора напряженности электрического поля $$\overrightarrow{E}$$

. После чего одновременно измеряют разность фаз между ними Δφ_RL=φ_R-φ_L и по измеренной разности фаз Δφ_RL рассчитывают угол крена γ ЛА между поперечной осью ЛА и горизонтальной плоскостью.On board the aircraft, the receiving antenna receives electromagnetic waves in a circular orthogonal in-phase polarization basis, in which the received electromagnetic waves are simultaneously divided into two components of the right orthogonally polarized in a circle $${\overrightarrow{E}}_R$$

and left $${\overrightarrow{E}}_L$$

direction of rotation of the electric field vector $$\overrightarrow{E}$$

. Then simultaneously measure the phase difference between them Δφ _RL = φ _R -φ _L and the measured angle of the phases Δφ _RL calculate the angle of heel γ LA between the transverse axis of the aircraft and the horizontal plane.

и левого $${\overrightarrow{E}}_L$$

направления вращения составляющих вектора электрического поля $$\overrightarrow{E}$$

и углом крена ЛА.Obviously, to measure the roll angle γ of an aircraft, it is necessary to establish a relationship between the phase difference Δφ _{RL of the} right-hand orthogonal polarized $${\overrightarrow{E}}_R$$

and left $${\overrightarrow{E}}_L$$

directions of rotation of the components of the electric field vector $$\overrightarrow{E}$$

and roll angle LA.

To establish this connection, we use the well-known [5–8] formalism of vectors and Jones matrices.

Since the reception of electromagnetic waves on board an aircraft is carried out in its own circular polarizing basis, where the received electromagnetic waves are divided into two circularly polarized waves with the opposite direction of rotation, let us visualize the radiated horizontally linearly polarized electromagnetic wave in a linear orthogonal polarizing basis in the form of the sum of such waves. Then we get:

$$\overrightarrow{\dot{E}}=\left[\begin{array}{c}{\dot{E}}_x\\ {\dot{E}}_y\end{array}\right]\cdot e^{j\omega t}=\left[\begin{array}{c}\frac{E_{m_x}}{2}{e}^{j\omega t}\\ \frac{E_{m_x}}{2}{e}^{j\left(\omega t-\frac{\pi }{2}\right)}\end{array}\right]+\left[\begin{array}{c}\frac{E_{m_x}}{2}{e}^{j\omega t}\\ \frac{E_{m_x}}{2}{e}^{j\left(\omega t+\frac{\pi }{2}\right)}\end{array}\right],\left(\mathrm{one}\right)$$

, $${\dot{E}}_y$$

- комплексные амплитуды двух проекций электрического поля $$\overrightarrow{E}$$

на оси декартовой системы прямоугольных координат,Where $${\dot{E}}_x$$

, $${\dot{E}}_y$$

- complex amplitudes of two projections of the electric field $$\overrightarrow{E}$$

on the axis of the Cartesian system of rectangular coordinates,

ω is the circular frequency

t is time.

вектора электрического поля, в то время как вторая группа составляющих представляет волну, поляризованную по кругу с правым $${\overrightarrow{E}}_R$$

направлением вращения вектора электрического поля. При этом необходимо отметить, что направление вращения поляризации определено с точки зрения наблюдателя, рассматривающего волну против ее распространения. Подставляя в (1) t=0 и $$E_{m_x}=1$$

, а также используя формализм векторов Джонса [5-8], получим выражение для вектора Джонса $$\dot{\overrightarrow{E}}$$

излучаемых электромагнитных волн в линейном ортогональном поляризационном базисе в виде:Analyzing (1), we see that the first group of components is an electromagnetic wave polarized in a circle with the left direction of rotation $${\overrightarrow{E}}_L$$

of the electric field vector, while the second group of components represents a wave polarized in a circle with the right $${\overrightarrow{E}}_R$$

direction of rotation of the electric field vector. It should be noted that the direction of rotation of the polarization is determined from the point of view of the observer viewing the wave against its propagation. Substituting in (1) t = 0 and $$E_{m_x}=\mathrm{one}$$

, and also using the Jones vector formalism [5-8], we obtain the expression for the Jones vector $$\dot{\overrightarrow{E}}$$

radiated electromagnetic waves in a linear orthogonal polarizing basis in the form of:

$$\overrightarrow{E}=\left[\begin{array}{c}\mathrm{one}\\ 0\end{array}\right]=\frac{\mathrm{one}}{2}\left\{\left[\begin{array}{c}\mathrm{one}\\ -j\end{array}\right]+\left[\begin{array}{c}\mathrm{one}\\ j\end{array}\right]\right\}.\left(2\right)$$

Then the Jones vector of the received linearly horizontally polarized electromagnetic wave (2) defined by its projections in a linear polarization basis by the sum of two waves polarized in a circle with the opposite direction of rotation of the electric field vector can be determined on board the aircraft with positive + γ or negative -γ roll, when switching to a circular in-phase orthogonal polarizing basis at the input of the receiver in the form:

$${\dot{\overrightarrow{E}}}_{RL}=\left[\begin{array}{c}{\overrightarrow{\dot{E}}}_L\\ {\overrightarrow{\dot{E}}}_R\end{array}\right]=\frac{\mathrm{one}}{\sqrt{2}}\cdot \left[\begin{array}{cc}\mathrm{one}& j\\ \mathrm{one}& -j\end{array}\right]\cdot \left[\begin{array}{cc}-\cos \gamma & \pm \sin \gamma \\ \mp \sin \gamma & \cos \gamma \end{array}\right]\cdot \overrightarrow{E},\left(3\right)$$

- вектор Джонса $$\dot{\overrightarrow{E}}$$

излучаемых электромагнитных волн, заданный своими проекциями в линейном ортогональном поляризационном базисе в виде суммы двух волн, поляризованных по кругу с противоположным направлением вращения,Where $$\dot{\overrightarrow{E}}=\frac{\mathrm{one}}{2}\left\{\left[\begin{array}{c}\mathrm{one}\\ -j\end{array}\right]+\left[\begin{array}{c}\mathrm{one}\\ j\end{array}\right]\right\}$$

- jones vector $$\dot{\overrightarrow{E}}$$

radiated electromagnetic waves, given by their projections in a linear orthogonal polarization basis in the form of the sum of two waves polarized in a circle with the opposite direction of rotation,

- оператор перехода из линейного поляризационного базиса, в котором записан вектор Джонса $$\overrightarrow{E}$$

излучаемых электромагнитных волн, в линейный поляризационный базис, повернутый на произвольный угол крена ±γ относительно исходного, $$\left[\begin{array}{cc}-\cos \gamma & \pm \sin \gamma \\ \mp \sin \gamma & \cos \gamma \end{array}\right]$$

is the transition operator from a linear polarization basis in which the Jones vector is written $$\overrightarrow{E}$$

radiated electromagnetic waves, into a linear polarization basis, rotated by an arbitrary angle of heel ± γ relative to the original,

± γ - corresponds to the positive angle of the aircraft roll, when its right wing or transverse axis is below the horizontal plane,

-γ - corresponds to the negative roll angle of the aircraft when its right wing or transverse axis is above the horizontal plane,

- оператор перехода из линейного поляризационного базиса повернутого на произвольный угол крена ±γ относительно исходного в синфазный круговой поляризационный базис, в котором базисные единичные векторы соответствуют волнам с левой и правой круговой поляризацией, электрические векторы которых в момент времени t=0 совпадают с направлением вектора электрического поля $$\overrightarrow{E}$$

. $$\left[\begin{array}{cc}\mathrm{one}& j\\ \mathrm{one}& -j\end{array}\right]$$

is the operator of the transition from a linear polarization basis rotated by an arbitrary angle of angle ± γ relative to the initial one into a common-mode circular polarization basis, in which basic unit vectors correspond to waves with left and right circular polarization, the electric vectors of which at time t = 0 coincide with the direction of the electric vector fields $$\overrightarrow{E}$$

.

и левого $${\dot{\overrightarrow{E}}}_L$$

направления вращения вектора электрического поля $$\overrightarrow{E}$$

на входе приемника в виде:After the transformations, we obtain analytic expressions for the components of the right orthogonally polarized in a circle $${\dot{\overrightarrow{E}}}_R$$

and left $${\dot{\overrightarrow{E}}}_L$$

direction of rotation of the electric field vector $$\overrightarrow{E}$$

at the input of the receiver in the form:

$${\dot{\overrightarrow{E}}}_L=\frac{\mathrm{one}}{2\sqrt{2}}\cdot \left[\begin{array}{cc}\mathrm{one}& j\\ \mathrm{one}& -j\end{array}\right]\cdot \left[\begin{array}{cc}-\cos \gamma & \pm \sin \gamma \\ \mp \sin \gamma & \cos \gamma \end{array}\right]\cdot \left[\begin{array}{c}\mathrm{one}\\ -j\end{array}\right],\left(\mathrm{four}\right)$$

$${\dot{\overrightarrow{E}}}_R=\frac{\mathrm{one}}{2\sqrt{2}}\cdot \left[\begin{array}{cc}\mathrm{one}& j\\ \mathrm{one}& -j\end{array}\right]\cdot \left[\begin{array}{cc}-\cos \gamma & \pm \sin \gamma \\ \mp \sin \gamma & \cos \gamma \end{array}\right]\cdot \left[\begin{array}{c}\mathrm{one}\\ -j\end{array}\right].\left(5\right)$$

, и $${\dot{\overrightarrow{E}}}_R$$

на входе приемника в виде:Substituting the values + γ in (4) and (5), we obtain, respectively, the expressions for $${\dot{\overrightarrow{E}}}_L$$

, and $${\dot{\overrightarrow{E}}}_R$$

at the input of the receiver in the form:

$${\dot{\overrightarrow{E}}}_L=\frac{\mathrm{one}}{\sqrt{2}}\left(\cos \gamma -j\sin \gamma \right),\left(6\right)$$

$${\dot{\overrightarrow{E}}}_R=\frac{\mathrm{one}}{\sqrt{2}}\left(\cos \gamma +j\sin \gamma \right).\left(7\right)$$

и $${\dot{E}}_R$$

на выходе приемника имеют вид:Using the known relations [7], the amplitudes A _L and A _R , as well as the phases φ _L and φ _R of the components orthogonally polarized in a circle $${\dot{E}}_L$$

and $${\dot{E}}_R$$

at the output of the receiver are:

$$A_L=\frac{\mathrm{one}}{\sqrt{2}},\left(8\right)$$

$${\varphi }_L=-arctg\frac{\sin \gamma }{\cos \gamma },\left(9\right)$$

$$A_R=\frac{\mathrm{one}}{\sqrt{2}},\left(10\right)$$

$${\varphi }_R=-arctg\frac{\sin \gamma }{\cos \gamma },\left(\mathrm{eleven}\right)$$

and their phase difference after transformations has the form:

$$\Delta {\varphi }_{RL}={\varphi }_R-{\varphi }_L=2\gamma ,\left(12\right)$$

whence it follows that

$$\gamma =\frac{\Delta {\varphi }_{R\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="00000096.png"\; state="\{\{state\}\}">L</figure-callout>}}}{2}.\left(13\right)$$

и $${\dot{E}}_R$$

на выходе приемника равны между собой A_L=A_R и не зависят от угла крена γ ЛА. В то же время из анализа (13) видно, что наличие фазового сдвига между ортогональными волнами круговой поляризации обусловлено углом крена γ ЛА.From the analysis of (8) and (10) it follows that the amplitudes A _L and A _R of the components orthogonally polarized in a circle $${\dot{E}}_L$$

and $${\dot{E}}_R$$

at the receiver output, A _L = A _R are equal to each other and are independent of the angle of heel γ LA. At the same time, it is seen from analysis (13) that the presence of a phase shift between orthogonal waves of circular polarization is due to the angle of heel γ LA.

и $${\dot{E}}_R$$

на входе приемника в виде:Substituting the value -γ in (4) and (5) or in (6) and (7), we obtain the expressions for $${\dot{E}}_L$$

and $${\dot{E}}_R$$

at the input of the receiver in the form:

$${\dot{\overrightarrow{E}}}_L=\frac{\mathrm{one}}{\sqrt{2}}\left(\cos \gamma +j\sin \gamma \right),\left(\mathrm{fourteen}\right)$$

$${\dot{\overrightarrow{E}}}_R=\frac{\mathrm{one}}{\sqrt{2}}\left(\cos \gamma -j\sin \gamma \right),\left(\mathrm{fifteen}\right)$$

и $${\dot{E}}_R$$

на выходе имеют вид:Accordingly, the amplitudes A _L and A _R , as well as the phases φ _L and φ _R of the components orthogonally polarized in a circle $${\dot{E}}_L$$

and $${\dot{E}}_R$$

at the output they have the form:

$$A_L=\frac{\mathrm{one}}{\sqrt{2}},\left(16\right)$$

$${\varphi }_L=-arctg\frac{\sin \gamma }{\cos \gamma },\left(17\right)$$

$$A_R=\frac{\mathrm{one}}{\sqrt{2}},\left(\mathrm{eighteen}\right)$$

$${\varphi }_R=-arctg\frac{\sin \gamma }{\cos \gamma },\left(\mathrm{eighteen}\right)$$

and their phase difference after transformations has the form:

$$\Delta {\varphi }_{RL}={\varphi }_R-{\varphi }_L=-2\gamma ,\left(19\right)$$

whence it follows that

$$\gamma =-\frac{\Delta {\varphi }_{R\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="00000096.png"\; state="\{\{state\}\}">L</figure-callout>}}}{2}.\left(\mathrm{twenty}\right)$$

и $${\dot{E}}_R$$

для отрицательных углов крена -γ также равны между собой A_L=A_R и не зависят от угла крена γ ЛА. В то же время разность фаз Δφ_RL (20) определяется углом крена γ ЛА. Сравнивая (13) и (20), окончательно имеем выражение для определения угла крена γ ЛА в виде:From the analysis of (16) and (18) it follows that at the output of the receiver, the amplitudes A _L and A _R of the components orthogonally polarized in a circle $${\dot{E}}_L$$

and $${\dot{E}}_R$$

for negative heeling angles, -γ are also equal to each other A _L = A _R and are independent of the heeling angle γ LA. At the same time, the phase difference Δφ _RL (20) is determined by the angle of heel γ LA. Comparing (13) and (20), we finally have an expression for determining the roll angle γ of an aircraft in the form:

$$\gamma =\pm \frac{\Delta {\mathrm{<figure-callout\; id="2"\; label="\phi \; R\; L"\; filenames="00000096.png"\; state="\{\{state\}\}">\varphi \; </figure-callout>}}_{RL}}{2},\left(21\right)$$

where "+" - corresponds to a positive angle of heel γ, when the right wing or the transverse axis of the aircraft is below the horizontal plane,

“-” - corresponds to the negative angle of the aircraft roll, when its right wing or transverse axis is above the horizontal plane,

и $${\dot{E}}_R$$

.Δφ _RL = φ _R -φ _L is the phase difference between orthogonally circularly polarized waves $${\dot{E}}_L$$

and $${\dot{E}}_R$$

.

и $${\dot{E}}_R$$

на входе приемной антенны, что неизменно приводит к изменению угла ориентации вектора напряженности электрического поля $$\overrightarrow{E}$$

принимаемых на борту ЛА электромагнитных волн, или, иначе говоря, одновременно изменяется ориентация плоскости поляризации принимаемых электромагнитных волн. Последнее определяет физическую основу для определения угла крена ЛА по измеренной на выходе приемника разности фаз Δφ_RL между ортогонально поляризованными по кругу составляющими $${\dot{E}}_L$$

и $${\dot{E}}_R$$

.Thus, conducting a comparative analysis of the obtained expressions (12) and (19), we see that when the roll of the aircraft occurs, a phase shift occurs between the orthogonally circularly polarized components $${\dot{E}}_L$$

and $${\dot{E}}_R$$

at the input of the receiving antenna, which invariably leads to a change in the orientation angle of the electric field strength vector $$\overrightarrow{E}$$

the electromagnetic waves received on board the aircraft, or, in other words, the orientation of the plane of polarization of the received electromagnetic waves changes simultaneously. The latter determines the physical basis for determining the roll angle of an aircraft from the phase difference Δφ _RL measured at the receiver output between the components orthogonally polarized in a circle $${\dot{E}}_L$$

and $${\dot{E}}_R$$

.

The use of the claimed combination of features for measuring the roll angle of an aircraft in known solutions by the author was not found.

Figure 1 presents the structural electrical diagram of a device that implements the proposed method for measuring the angle of heel of the aircraft.

The device comprises a transmitter 1 and a transmitting antenna 2 located at a point with known coordinates. On board the aircraft, the device comprises a receiving antenna 3, a circular waveguide section with a built-in quarter-wave phase plate 4, a linear polarizing separator 5, a phase angular discriminator 6, and an indicator 7.

Figure 2 presents the structural electrical diagram of the phase angular discriminator 6, which includes the first and second frequency mixers 8 and 9, the first intermediate frequency amplifier (IFA) with an amplitude limit of 10, local oscillator 11, and a second intermediate frequency amplifier (IFA) with a limit amplitude 13, phase shifter 90 ° 12, phase detector 14.

The device operates as follows.

The transmitter 1 through the transmitting antenna 2 emits horizontally linearly polarized electromagnetic waves in the direction of the aircraft, the electric field vector E of which coincides with the horizontal plane and is defined by its projections in the linear polarization basis as the sum of two waves orthogonally polarized in a circle in the form (2).

On board an aircraft with a generally positive + γ or negative -γ angle of heel, electromagnetic waves, the Jones vector of which is of the form (2), are received by the receiving antenna 3 and fed to the serially connected section of the circular waveguide with a quarter-wave phase plate built into the inside 4 and a linear polarizing separator 5, made in the form of a transition from a circular waveguide to two rectangular waveguides orthogonally located relative to each other, whose unit coordinates of the coordinate system coincide axes shoulders rectangular waveguides and also coincide with the vertical and transversal axes of the aircraft respectively. Moreover, the quarter-wave phase plate is oriented at an angle θ = -45 ° to one of the walls of the rectangular waveguide of the linear polarizing separator 5. The combination of the circular waveguide section with the quarter-wave phase plate 4 embedded in the inside and the linear polarizing separator 5 allows, as is known [7], to realize board the aircraft receiving electromagnetic waves in a circular polarizing basis and, thus, divide the electromagnetic waves coming into the input, the Jones vector of which is given in the form (2), into two orthogonally olyarizovannye circular waves. In this case, the signals at the outputs of the arms of the linear polarizing separator 5 are determined using transformations of the form:

$${\overrightarrow{\dot{E}}}_x=\left[\begin{array}{cc}\mathrm{one}& 0\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]\cdot \left[\begin{array}{cc}\mathrm{one}& 0\\ 0& j\end{array}\right]\cdot \left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right]\cdot \left[\begin{array}{cc}\cos \gamma & \pm \sin \gamma \\ \mp \sin \gamma & \cos \gamma \end{array}\right]\cdot \overrightarrow{E},\left(22\right)$$

$${\overrightarrow{\dot{E}}}_y=\left[\begin{array}{cc}0& 0\\ 0& \mathrm{one}\end{array}\right]\cdot \left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]\cdot \left[\begin{array}{cc}\mathrm{one}& 0\\ 0& j\end{array}\right]\cdot \left[\begin{array}{cc}-\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right]\cdot \left[\begin{array}{cc}\cos \gamma & \pm \sin \gamma \\ \mp \sin \gamma & \cos \gamma \end{array}\right]\cdot \overrightarrow{E},\left(23\right)$$

- вектор Джонса $$\overrightarrow{E}$$

излучаемых электромагнитных волн, заданный своими проекциями в линейном поляризационном базисе в виде суммы двух волн, ортогонально поляризованных по кругу,Where $$\dot{\overrightarrow{E}}=\frac{\mathrm{one}}{2}\left\{\left[\begin{array}{c}\mathrm{one}\\ -j\end{array}\right]+\left[\begin{array}{c}\mathrm{one}\\ j\end{array}\right]\right\}$$

- jones vector $$\overrightarrow{E}$$

radiated electromagnetic waves, given by their projections in a linear polarizing basis in the form of the sum of two waves orthogonally polarized in a circle,

- оператор перехода из линейного поляризационного оазиса, в котором записан вектор Джонса $$\overrightarrow{E}$$

излучаемых электромагнитных волн, в линейный поляризационный базис, повернутый на произвольный угол крена ±γ относительно исходного, $$\left[\begin{array}{cc}\cos \gamma & \pm \sin \gamma \\ \mp \sin \gamma & \cos \gamma \end{array}\right]$$

is the transition operator from a linear polarizing oasis in which the Jones vector is written $$\overrightarrow{E}$$

radiated electromagnetic waves, into a linear polarization basis, rotated by an arbitrary angle of heel ± γ relative to the original,

- оператор Джонса четвертьволновой фазовой пластины, записанный в собственной системе координат, в которой он имеет диагональный вид, $$\left[\begin{array}{cc}\mathrm{one}& 0\\ 0& -j\end{array}\right]$$

- Jones operator quarter-wave phase plate, recorded in its own coordinate system in which it has a diagonal form,

- обратный оператор перехода из собственной системы координат четвертьволновой фазовой пластины в опорную систему координат, в которой представлен вектор Джонса $$\overrightarrow{E}$$

излучаемых электромагнитных волн, $$\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$$

- the inverse transition operator from the own coordinate system of the quarter-wave phase plate to the reference coordinate system, in which the Jones vector $$\overrightarrow{E}$$

radiated electromagnetic waves,

- оператор первого плеча линейного поляризационного разделителя (переход с круглого волновода на прямоугольный), собственная поляризация которого совпадает с вектором $$\overrightarrow{E}$$

, $$\left[\begin{array}{cc}\mathrm{one}& 0\\ 0& 0\end{array}\right]$$

- the operator of the first shoulder of the linear polarization separator (transition from a circular waveguide to a rectangular one), whose intrinsic polarization coincides with the vector $$\overrightarrow{E}$$

,

- оператор второго плеча линейного поляризационного разделителя, собственная поляризация которого ортогональна вектору $$\overrightarrow{E}$$

. $$\left[\begin{array}{cc}0& 0\\ 0& \mathrm{one}\end{array}\right]$$

is the operator of the second arm of the linear polarization separator, whose intrinsic polarization is orthogonal to the vector $$\overrightarrow{E}$$

.

и $${\dot{\overrightarrow{E}}}_y$$

на выходах линейного поляризационного разделителя 5 вида:Substituting the values + γ and θ = -45 ° in (22) and (23), and having completed the necessary matrix transformations, we obtain analytical expressions for orthogonally linearly polarized signals $${\dot{\overrightarrow{E}}}_x$$

and $${\dot{\overrightarrow{E}}}_y$$

at the outputs of the linear polarizing separator 5 of the form:

$${\dot{\overrightarrow{E}}}_x=\frac{\mathrm{one}}{2}\{(\cos \gamma +\sin \gamma )+j(\cos \gamma -\sin \gamma )\},\left(24\right)$$

$${\dot{\overrightarrow{E}}}_y=\frac{\mathrm{one}}{2}\{\cos \gamma +\sin \gamma )+j(\cos \gamma -\sin \gamma )\}.\left(25\right)$$

излучаемых горизонтально линейно поляризованных электромагнитных волн представлен своими проекциями в линейном ортогональном поляризационном базисе в виде суммы двух волн ортогонально поляризованных по кругу с левым $${\dot{\overrightarrow{E}}}_L$$

и правым $${\dot{\overrightarrow{E}}}_R$$

направлением вращения вектора электрического поля, которые, с учетом введенного в радиолокационный канал угла крена ЛА, принимаются на борту ЛА приемной антенной 2 и поступают на вход секции круглого волновода со встроенной во внутрь четвертьволновой фазовой пластиной. При прохождении этой секции ортогонально поляризованные по кругу электромагнитные волны $${\dot{\overrightarrow{E}}}_L$$

и $${\dot{\overrightarrow{E}}}_R$$

на выходе секции преобразуются, как известно [7], в линейно ортогонально поляризованные электромагнитные волны $${\overrightarrow{\dot{E}}}_x$$

и $${\overrightarrow{\dot{E}}}_y$$

с горизонтальной и вертикальной поляризациями соответственно и имеют, с учетом (22) и (23), вид:It is appropriate to explain the essence of the obtained expressions (24) and (25). For this, we turn to relation (2), from which it follows that the Jones vector $$\overrightarrow{E}$$

radiated horizontally linearly polarized electromagnetic waves is represented by its projections in a linear orthogonal polarization basis in the form of the sum of two waves orthogonally polarized in a circle with the left $${\dot{\overrightarrow{E}}}_L$$

and right $${\dot{\overrightarrow{E}}}_R$$

the direction of rotation of the electric field vector, which, taking into account the angle of heel of the aircraft entered into the radar channel, is received on board the aircraft by the receiving antenna 2 and arrives at the input of the circular waveguide section with a quarter-wave phase plate built into the inside. When passing through this section, electromagnetic waves orthogonally polarized in a circle $${\dot{\overrightarrow{E}}}_L$$

and $${\dot{\overrightarrow{E}}}_R$$

at the output of the section, as is known [7], they are transformed into linearly orthogonally polarized electromagnetic waves $${\overrightarrow{\dot{E}}}_x$$

and $${\overrightarrow{\dot{E}}}_y$$

with horizontal and vertical polarizations, respectively, and have, taking into account (22) and (23), the form:

$${\dot{\overrightarrow{E}}}_x=\frac{\mathrm{one}}{2}\left[\begin{array}{c}\left(\cos \gamma +\sin \gamma \right)+j\left(\cos \gamma -\sin \gamma \right)\\ 0\end{array}\right],\left(26\right)$$

and

$${\dot{\overrightarrow{E}}}_y=\frac{\mathrm{one}}{2}\left[\begin{array}{c}\left(\cos \gamma +\sin \gamma \right)+j\left(\cos \gamma -\sin \gamma \right)\\ 0\end{array}\right].\left(27\right)$$

и $${\dot{\overrightarrow{E}}}_y$$

и будут характеризовать собой амплитуды A_L и A_R, a также фазы φ_L, и φ_R ортогонально поляризованных по кругу составляющих $${\overrightarrow{\dot{E}}}_L$$

и $${\overrightarrow{\dot{E}}}_R$$

соответственно. Тогда используя известные соотношения [7]. найдем амплитуды A_x и A_y, а также фазы φ_x и φ_y ортогонально линейно поляризованных сигналов $${\dot{\overrightarrow{E}}}_x$$

и $${\dot{\overrightarrow{E}}}_y$$

на выходе линейного поляризационного разделителя 5:From the output of the circular waveguide section with the quarter-wave phase plate integrated inside, the signals (26) and (27) are fed to the corresponding inputs of the rectangular waveguides of the linear polarizing splitter 5. Thus, at the output of the linear polarizing splitter 5, orthogonally linearly polarized signals are formed having the form ( 24) and (25). Moreover, as is known [7], the amplitudes A _x and A _y , as well as the phases φ _x and φ _{y of} these orthogonally linearly polarized components $${\dot{\overrightarrow{E}}}_x$$

and $${\dot{\overrightarrow{E}}}_y$$

and will characterize the amplitudes A _L and A _R , as well as the phases φ _L , and φ _R of the components orthogonally polarized in a circle $${\overrightarrow{\dot{E}}}_L$$

and $${\overrightarrow{\dot{E}}}_R$$

respectively. Then using the known relations [7]. we find the amplitudes A _x and A _y , as well as the phases φ _x and φ _{y of the} orthogonally linearly polarized signals $${\dot{\overrightarrow{E}}}_x$$

and $${\dot{\overrightarrow{E}}}_y$$

at the output of the linear polarizing separator 5:

$$A_x=\frac{\sqrt{2}}{2},\left(28\right)$$

$${\varphi }_x=45-\gamma ,\left(\mathrm{29th}\right)$$

$$A_y=\frac{\sqrt{2}}{2},\left(\mathrm{thirty}\right)$$

$${\varphi }_y=-\left(45-\gamma \right),\left(31\right)$$

and their phase difference

$$\Delta {\varphi }_{yx}={\varphi }_y-{\varphi }_x=-90+2\gamma ,\left(32\right)$$

постоянного фазового сдвига 90°, окончательно получим:or, taking into account input to the channel $${\dot{E}}_y$$

constant phase shift of 90 °, we finally get:

$$\gamma =-\frac{\Delta {\mathrm{<figure-callout\; id="2"\; label="\phi \; y\; x"\; filenames="00000096.png"\; state="\{\{state\}\}">\varphi \; </figure-callout>}}_{yx}}{2}.\left(33\right)$$

и $${\dot{\overrightarrow{E}}}_y$$

на выходе линейного поляризационного разделителя 5 постоянны, равны между собой A_x-A_y и не зависят от угла крена γ ЛА. В то же время фазовый сдвиг Δφ_yx между сигналами $${\dot{\overrightarrow{E}}}_x$$

и $${\dot{\overrightarrow{E}}}_y$$

на выходе линейного поляризационного разделителя определяется углом крена γ ЛА.From the analysis of (28) and (30) it follows that the amplitudes A _x and A _{y of the} orthogonally linearly polarized components $${\dot{\overrightarrow{E}}}_x$$

and $${\dot{\overrightarrow{E}}}_y$$

at the output of the linear polarizing separator 5 are constant, equal to each other A _x -A _y and do not depend on the angle of heel γ LA. At the same time, the phase shift Δφ _yx between the signals $${\dot{\overrightarrow{E}}}_x$$

and $${\dot{\overrightarrow{E}}}_y$$

the output of the linear polarizing separator is determined by the angle of heel γ LA.

и $${\dot{\overrightarrow{E}}}_y$$

на выходе линейного поляризационного разделителя в виде:Substituting the values of γ in (22) and (23) or in (24) and (25), we obtain expressions for orthogonally linearly polarized signals $${\dot{\overrightarrow{E}}}_x$$

and $${\dot{\overrightarrow{E}}}_y$$

at the output of the linear polarizing separator in the form:

$${\dot{\overrightarrow{E}}}_x=\frac{\mathrm{one}}{2}\{(\cos \gamma -\sin \gamma )+j(\cos \gamma +\sin \gamma )\},\left(34\right)$$

$${\dot{\overrightarrow{E}}}_y=\frac{\mathrm{one}}{2}\{-(\cos \gamma -\sin \gamma )+j(\cos \gamma +\sin \gamma )\}.\left(35\right)$$

и $${\dot{\overrightarrow{E}}}_y$$

на выходе линейного поляризационного разделителя 5 имеют вид:Accordingly, the amplitudes A _x and A _y , as well as the phases φ _x and φ _{y of the} orthogonally polarized signals $${\dot{\overrightarrow{E}}}_x$$

and $${\dot{\overrightarrow{E}}}_y$$

the output of the linear polarizing separator 5 are of the form:

$$A_x=\frac{\sqrt{2}}{2},\left(36\right)$$

$${\varphi }_x=45+\gamma ,\left(37\right)$$

$$A_y=\frac{\sqrt{2}}{2},\left(38\right)$$

$${\varphi }_y=-\left(45+\gamma \right),\left(39\right)$$

and their phase difference:

$$\Delta {\varphi }_{yx}={\varphi }_y-{\varphi }_x=-90-2\gamma ,\left(40\right)$$

, окончательно получим:or, taking into account the constant phase shift of 90 ° in the channel $${\dot{E}}_y$$

, we finally get:

$$\gamma =-\frac{\Delta {\mathrm{<figure-callout\; id="2"\; label="\phi \; y\; x"\; filenames="00000096.png"\; state="\{\{state\}\}">\varphi \; </figure-callout>}}_{yx}}{2}.\left(41\right)$$

и $${\dot{\overrightarrow{E}}}_y$$

на выходе линейного поляризационного разделителя 5 для отрицательных углов крена -γ также, как и для положительных углов крена +γ постоянны и равны между собой A_xx=A_y и не зависят от угла крена γ ЛА. В то же время разность фаз Δφ_yx (41) определяется только углом крена γ ЛА. Сравнивая (33) и (41), окончательно получим выражение для определения угла крена γ ЛА в виде:From the analysis of (36) and (38) it follows that the amplitudes A _x and A _{y of} orthogonally linearly polarized signals $${\dot{\overrightarrow{E}}}_x$$

and $${\dot{\overrightarrow{E}}}_y$$

at the output of the linear polarizing separator 5 for negative roll angles −γ, as well as for positive roll angles + γ, A _xx = A _y are constant and equal to each other and are independent of the roll angle γ of the aircraft. At the same time, the phase difference Δφ _yx (41) is determined only by the roll angle γ of the aircraft. Comparing (33) and (41), we finally obtain the expression for determining the roll angle γ of the aircraft in the form:

$$\gamma =\pm \frac{\Delta {\phi }_{yx}}{2}.\left(42\right)$$

where "+" - corresponds to a positive angle of heel γ, when the right wing or the transverse axis of the aircraft is below the horizontal plane,

“-” - corresponds to the negative angle of heel γ, when the right wing or the transverse axis of the aircraft is below the horizontal plane,

и $${\dot{\overrightarrow{E}}}_y$$

на выходе линейного поляризационного разделителя.Δφ _yx = φ _y- φ _x is the phase difference between orthogonally linearly polarized signals $${\dot{\overrightarrow{E}}}_x$$

and $${\dot{\overrightarrow{E}}}_y$$

at the output of a linear polarizing separator.

и $${\dot{\overrightarrow{E}}}_y$$

поступают на входы фазового углового дискриминатора 6 (см. фиг.2), т.е. поступают соответственно на первые входы смесителей частоты 8 и 9, а на их вторые входы поступает сигнал с выхода гетеродина 11. После чего сигнал $${\dot{\overrightarrow{E}}}_x$$

с выхода первого смесителя частоты 8 поступает на вход первого УПЧ с ограничением по амплитуде 10, а сигнал $${\dot{\overrightarrow{E}}}_y$$

с выхода второго смесителя частоты 9 через фазовращатель на 90° 12 поступает на вход второго УПЧ с ограничением по амплитуде 13. В УПЧ 10 и 13, имеющих идентичные амплитудно-фазочастотные характеристики, осуществляется усиление сигналов промежуточной частоты, а также производится их нормировка за счет амплитудного ограничения усиливаемых сигналов промежуточной частоты с порогом ограничения U₀. Затем выходной сигнал УПЧ 10 поступает на первый вход фазового детектора 14, а выходной сигнал УПЧ 13 поступает на второй вход фазового детектора 14. На выходе фазового детектора 14 формируется сигнал, пропорциональный синусу разности фаз Δφ_yx=φ_y-φ_x входных сигналов, и имеет вид:From the outputs of the shoulders of the linear polarizing splitter 5 orthogonally linearly polarized signals $${\dot{\overrightarrow{E}}}_x$$

and $${\dot{\overrightarrow{E}}}_y$$

arrive at the inputs of the phase angular discriminator 6 (see figure 2), i.e. respectively arrive at the first inputs of the frequency mixers 8 and 9, and their second inputs receive a signal from the output of the local oscillator 11. After that, the signal $${\dot{\overrightarrow{E}}}_x$$

from the output of the first frequency mixer 8 is fed to the input of the first amplifier with a limitation in amplitude of 10, and the signal $${\dot{\overrightarrow{E}}}_y$$

from the output of the second frequency mixer 9, through a phase shifter 90 ° 12 is supplied to the input of the second amplifier with a limit on the amplitude of 13. In the amplifiers 10 and 13, which have identical amplitude-phase-frequency characteristics, the signals of the intermediate frequency are amplified, and they are also normalized due to the amplitude limiting amplified signals of intermediate frequency with a limiting threshold U ₀ Then, the output signal of the amplifier 10 is supplied to the first input of the phase detector 14, and the output signal of the amplifier 10 is supplied to the second input of the phase detector 14. At the output of the phase detector 14, a signal is generated proportional to the sine of the phase difference Δφ _yx = φ _y- φ _{x of the} input signals, and has the form:

$$S\left(\gamma \right)=U_0\cdot \sin \left({\phi }_y-{\phi }_x\right)\left(43\right)$$

or considering (42)

$$S\left(\gamma \right)=U_0\cdot \sin \left(\pm 2\gamma \right),\left(44\right)$$

where U ₀ = const.

From the output of the phase detector 14, the signal is fed to the input of the indicator 7, the scale of which is graduated, taking into account (44) in degrees of roll angle γ LA.

In the 3 cm wavelength range of the inventive device for measuring the angle of heel of the aircraft can be performed as follows.

As the transmitter 1 can be used, for example, a standard generator of high-frequency oscillations of the type ГЧ-83.

As the transmitting antenna 2 can be used horn antenna [9], which has its own linear horizontal polarization.

The receiving antenna 3 can be made in the form of a round horn [10].

Linear polarizing separator 5 is made in the form of a waveguide of circular cross section with the transition to two orthogonally located waveguides of rectangular cross section [7].

The phase angular discriminator can be performed according to the well-known scheme [11] of a phase-phase monopulse system.

Indicator 7 can be made in the form of a pointer device, the scale of which is calibrated in degrees of the angle of heel of the aircraft.

Compared with the widely used means of measuring the angle of heel of an aircraft, based on the use of gyroscopic orientation systems, the inventive method and device for measuring the angle of heel of an aircraft allow to avoid the constant accumulation of measurement errors over time.

Information sources

1. A.S. Aleksandrov, G.R.Arno and others. The current state and development trends of foreign means and navigation systems of moving objects of military and civil purposes. - St. Petersburg, 1994 .-- 119 p.

2. D.S. Pelpor, V.V. Yagodkin. Gyroscopic systems. - M., Higher School, 1977 .-- 216 p.

3. Agadzhapov P.A., Vorobev V.G. et al. Automation of aircraft navigation and air traffic control. - M.: Transport, 1980 .-- 357 p.

4. Yarlykov M.S. Statistical theory of radio navigation. - M .: Radio and communications, 1985 .-- 344 p.

5. Kornblit S. microwave optics. Per. from English / Ed. O.P. Frolova. - M.: Communication, 1980 .-- 360 p.

6. Azzam R., Bashar P. Ellipsometry and polarized light. - M .: Mir, 1981. - 588 p.

7. Kanareikin DB, Potekhin V.A. Polarization of radar signals. - M .: “Owls. Radio ”, 1966. - 440 p.

8. Bogorodsky VV, Kanareikin DB, Kozlov A.I. Polarization of the scattered and intrinsic radio emission of the earth. - L .: Gidrometeoizdat, 1981. - 280 p.

9. Drabkin A.L. and other Antenna-feeder devices. - M .: “Owls. Radio ”, 1974. - 535 p.

10. Zhuk M.S., Molochkov Yu.B. Design of antenna-feeder devices. - M .: "Energy", 1966.

11. Leonov A.I., Fomichev K.I. Monopulse radar. - M.: “Radio and Communications”, 1984. - 312 p.

Claims (2)

1. A method of measuring the angle of heel of an aircraft when it moves to a source of electromagnetic wave radiation, characterized in that horizontally linearly polarized electromagnetic waves, an electric field vector, are emitted from a point with known coordinates $$\overrightarrow{E}$$

which coincides with the horizontal plane, receive electromagnetic waves on board the aircraft in their own in-phase circular polarization basis, the unit vectors of which correspond to waves with left and right circular polarization, the electric vectors of which at time t = 0 coincide with the direction of the electric field vector $$\overrightarrow{E}$$

, divide the received electromagnetic waves into two components of the right orthogonally polarized in a circle $${\overrightarrow{E}}_R$$

and left $${\overrightarrow{E}}_L$$

direction of rotation of the electric field vector $$\overrightarrow{E}$$

, measure the phase difference between them Δφ _RL , calculate the angle of heel γ between the transverse axis of the aircraft and the horizontal plane according to the formula
$$\gamma [gR\mathrm{but}d]=\pm \frac{\Delta {\varphi }_{RL}}{2}[gR\mathrm{but}d]$$

where Δφ _RL = φ _R -φ _L is the phase difference between the components of the right orthogonally polarized in a circle $${\overrightarrow{E}}_R$$

and left $${\overrightarrow{E}}_L$$

direction of rotation [hail],
+ γ is the positive angle of heel (the right wing, or the transverse axis of the aircraft, is below the horizontal plane),
-γ is the negative angle of heel (the right wing, or the transverse axis of the aircraft, is above the horizontal plane), 2. A device for measuring the roll angle of the aircraft, characterized in that at a point with known coordinates there is a transmitter whose output is connected to the input of the transmitting antenna with horizontal intrinsic polarization, and a receiving antenna located on board the aircraft, the output of which is connected to the input of the round section waveguide with a quarter-wave phase plate built into the inside, the output of which is connected to the input of the linear polarizing separator, the two outputs of which are connected to the corresponding the two inputs of the phase angular discriminator, the output of which is connected to the indicator input, the scale of which is calibrated in degrees of the roll angle of the aircraft, the electric field vector of the emitted horizontally linearly polarized electromagnetic waves coincides with the horizontal plane, the quarter-wave phase plate is oriented at an angle of -45 ° to the wide wall of the rectangular waveguide of one of the arms of the linear polarizing separator, and the linear polarizing separator is oriented so that its own unit vectors coincide with the vertical and transverse axes of the aircraft, respectively.

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