Based on the totality of measured geometric parameters, the system for determining the location of EMR sources is divided into:

· triangulation (goniometer, direction finding);

· difference-rangefinders;

· angular-difference-rangefinders.

The type and number of measured geometric quantities determine the spatial structure of the system for determining the location of the EMR source: the number of spatially separated receiving points of EMR source signals and the geometry of their location.

The triangulation (goniometer, direction finding) method is based on determining directions (bearings) to the EMR source at two points in space using radio direction finders spaced at base d (Fig. 18, a).

Rice. 18. Explanation of the triangulation method for determining the location of the EMR source on the plane (a) and in space (b)

If the EMR source is located in a horizontal or vertical plane, then to determine its location it is enough to measure two azimuth angles μ1 and μ2 (or two elevation angles). The location of the EMR source is determined by the intersection point of straight lines O1I and O2I - two position lines.

To determine the location of the source in space, measure the azimuth angles qa1 and qa2 at two spaced points O1 and O2 and the elevation angle qm1 at one of these points or, conversely, the elevation angles qm1 and qm2 at two receiving points and the azimuth angle qa1 at one of them (Fig. 18, b).

By calculation, the distance from one of the receiving points to the source can be determined using the measured angles and the known base value d:

from here we equate two expressions for h:

Thus, the distance to the source

The triangulation method is easy to technically implement. Therefore, it is widely used in radio and RTR systems, in passive radar diversity systems for detecting and determining the coordinates of emitting objects.

A significant disadvantage of the triangulation method is that with an increase in the number of EMR sources located in the coverage area of ​​radio direction finders, false detections of non-existent sources may occur (Fig. 19). As can be seen from Fig. 19, along with determining the coordinates of three true sources I1, I2 and I3, six false sources LI1, ..., LI6 are also detected. False detections can be eliminated when using the triangulation method by obtaining redundant information about direction-finding sources - by increasing the number of spaced radio direction finders or by identifying the received information as belonging to a specific source. Identification can be carried out by comparing signals received by direction finders by carrier frequency, repetition period and pulse duration

Rice. 19.

Additional information about sources is also obtained through cross-correlation processing of signals received at spaced points in space.

Elimination of false detections when using the triangulation method is also possible by obtaining data on the difference in distances from the radiation source to receiving points (locations of radio direction finders). If the point of intersection of the bearing lines does not lie on the hyperbola corresponding to the range difference, then it is false.

The difference-range-measuring method of location determination is based on measuring, using RES, the difference in distances from the EMR source to receiving points separated in space by a distance d. The location of the source on the plane is found as the intersection point of two hyperbolas (two range differences measured at three receiving points) belonging to different bases A1A2, A2A3 (Fig. 20). The focal points of the hyperbolas coincide with the locations of the reception points.

Rice. 20.

The spatial position of EMR sources is determined by three range differences, measured at three to four receiving points. The source location is the intersection point of three hyperboloids of revolution.

The goniometer-difference-rangefinder method of location determination involves measuring, using RES, the difference in distances from the EMR source to two spaced receiving points and measuring the direction to the source at one of these points.

To determine the coordinates of the source on the plane, it is enough to measure the azimuth μ and the difference in the ranges of the arterial pressure from the source to the receiving points. The location of the source is determined by the intersection point of the hyperbola and the straight line.

To determine the position of the source in space, it is necessary to additionally measure the elevation angle of the EMR source at one of the receiving points. The source location is found as the intersection point of the two planes and the surface of the hyperboloid.

Errors in determining the location of an EMR source on a plane depend on measurement errors of two geometric quantities:

· two bearings in triangulation systems;

· two range differences in difference rangefinder systems;

· one bearing and one range difference in angular-difference-rangefinder systems.

With a centered Gaussian law of distribution of errors in determining position lines, the root-mean-square value of the error in determining the location of the source is:

where are the variances of errors in determining position lines; r is the cross-correlation coefficient of random errors in determining the position lines L1 and L2; r - angle of intersection of position lines.

For independent errors in determining position lines, r = 0.

With the triangulation method of determining the location of the source

Root Mean Square Position Error

When using identical direction finders

The greatest accuracy will be when the position lines intersect at right angles (r = 90°).

When assessing errors in determining the location of a source in space, it is necessary to consider measurement errors of three geometric quantities. The location error depends in this case on the relative spatial orientation of the position surfaces. The highest accuracy of position determination will be when the normals to the position surfaces intersect at right angles.

Comparative assessment of difference-rangefinder and goniometric (direction-finding) methods for determining RES coordinates

In practice, to determine the coordinates of radio emission sources (ERS), goniometric (direction finding), rangefinder, sum-rangefinder, difference-rangefinder methods, as well as combinations thereof, are used.

From the description of these methods, their characteristic features can be identified.

Thus, to implement the rangefinder and total rangefinder methods, the structure of the signal must be known at receiving points. In this regard, among the types of RES listed above, such methods can only be used to locate subscriber terminals (AT) of cellular communications, since their operation is fundamentally possible only under the control of a base station, which always measures the range to the AT during radio communication.

For the angular-measuring (UM) and difference-range-measuring methods (RDM), information about the exact structure of the signal is not required, but it is enough to indicate only the region of the spectrum in which the main energy of the signal is concentrated. Moreover, more and more manufacturers of equipment for determining IR coordinates are paying attention to RDM, due to the advent of inexpensive compact computing resources and improved radio reception technologies, the availability of data transmission channels, as well as the presence of accurate distributed timing signals.

The table shows the results of an analysis of the advantages and disadvantages of traditional options for constructing RDM (with strict synchronization of peripheral receiving points) in comparison with PA, borrowed from the International Telecommunication Union report ITU-R SM.2211.

Table

Simpler requirements forantenna	The antenna is cheap, uncomplicated and can be small in size. RDM receivers can use one simple antenna (for example, a single-ended or balanced dipole). An additional advantage is that a low-profile antenna can be manufactured in a small size.
Easier site selection and calibration requirements	For RDM, the site selection requirements are less stringent than for PA, and virtually no calibration is required. As a result, deployment of RDM equipment is faster. Additional RDM receivers can be installed to overcome the effects of shadowing from tall obstacles. In a PA system, locations must be selected to minimize wavefront distortion caused by secondary radiation from local obstacles, ground reflections, and changes in soil conductivity.
Some PA system antenna arrays must be calibrated after installation on site in order to minimize the resulting frequency and direction dependent errors.	Wideband, low SNR and short duration signals The RDM method works effectively with new and emerging signals characterized by complex modulation methods, wide bandwidth and short duration. As the signal bandwidth increases, the efficiency of the RDM generally increases. The degree of PA efficiency, in approximation, does not depend on the signal bandwidth, provided that the spacing of the channels undergoing fast Fourier transform (FFT) is equal to the signal bandwidth. Both methods, RDM and AM, work more efficiently with signals that have higher SNRs and with longer integration times. The gain due to correlation processing allows RDM methods to detect and locate signals with low (and even negative) SNR. In addition, it allows you to use additional RDM receivers when determining geographic location. Low SNR signals can be processed using advanced PA techniques, such as correlation PA techniques with increased resolution or with auxiliary data (reference direction finding). Determining the geographic location of sources of short-duration signals requires the coordinated operation of receivers synchronized in time to a fraction of a value inversely proportional to the signal bandwidth. Providing such a possibility is an indispensable condition for the operation of RDM systems. In addition, RDM can determine geographic location based on very short duration measurements made on longer duration signals.
If the PA antenna elements are switched, then the required integration time will be less.	System complexity The receiver and antenna of the RDM system are simpler than the typical antenna array and two- or multi-channel receiver of the PA system.
The RDM system receiver requires at least one real-time RF channel for processing without delay and with maximum probability of signal interception (1) .	Suppression of uncorrelated noise and interference Advanced PA systems can mitigate the effects of uncorrelated and co-occurring co-frequency interference by using correlation with reference signals. Other advanced processing methods, such as MUSIC, can be robust to uncorrelated noise and interference. However, such methods require expensive computations and are not widely used in spectrum monitoring.
Mitigation of coherent co-frequency interference (multipath) under certain conditions	The degree of effectiveness of PA and RDM decreases in conditions of multipath - coherent interference at the same frequency. The impact of each method varies depending on the position of the sensor relative to the multipath reflections. With sufficient signal bandwidth, the RDM method is less sensitive to wave front distortion due to local obstacles (local multipath). Advanced signal processing may be required to eliminate position uncertainties caused by distant obstacles (remote multipath). Advanced processing can further filter correlation pairs used in RDM positioning and improve results in high multipath environments.
Advanced RDM processing can eliminate multipath time delays between measurement locations, providing high performance in challenging terrain.	Configuration Considerations RDM and UM provide the greatest accuracy when the IRI is located in the center of the perimeter formed by the measurement sites. The accuracy of determining the geographic location by the RDM method is determined by the geometric indicator of accuracy reduction, the quality of time synchronization and the quality of the RDM assessment. The accuracy of PA methods directly depends on the distance between the source and each PA receiver. The position uncertainty is a function of the uncertainty of the bearing angle and the distance from the receiver to the estimated position.
Position and bearing uncertainty increase with distance equally in both methods.	Highly suitable for use in RF sensor networks The RDM method is well suited for the deployment of many receivers.
Possibility of analysis in completely offline mode on a central server	RDM systems can store and record time-coordinated signal measurements from all receivers, so analysis can be performed completely offline on a central server. This includes spectral analysis of each receiver's signal, cross-correlation measurements, and geolocation. In PA systems, some signal measurements (such as direction finding results and direction finding accuracy) can also be stored and recorded on a central server.

These measurements are coordinated in time to the degree of time synchronization that is achievable in the PA system. Measurements such as spectral analysis and cross-correlation are not typical because they require the same trunk data rates as RDM.

(1) Typical correlation interferometry systems use time division to reduce the number of receivers required. These systems require two to three receivers connected to five, seven or more antennas. These systems are less complex than fully parallel direction finding systems, but require a longer minimum signal duration to determine position.

The qualitative analysis of the advantages and disadvantages of UM and RDM presented in the table at first glance indicates the preferability of using RDM for the implementation of the radio monitoring procedure. However, it cannot be said with certainty that this method will be preferable in all cases. Therefore, we will further conduct a more detailed comparison of these methods on a quantitative basis. To do this, we will use an indicator in the form of an error dispersion ellipse, which characterizes the spread of location errors with specific numerical indicators - the sizes of its minor and major semi-axes, as well as their slope. To construct a scattering ellipse centered at a point, the elements of the location accuracy matrix are first calculated . The inverse of the accuracy matrix is ​​the correlation matrix of coordinate calculation errors corresponding to the Rao-Kramer boundary

, where is the dispersion along the axis, is the correlation moment, and is the dispersion along the axis.

(1)

The elements of the accuracy matrix for the mind are calculated using the formulas: Where on a plane, is the root mean square error (RMS) of bearing estimation, radians.

For RDM positioning, the elements of the accuracy matrix are calculated through the matrix product.

This method is based on distance measurement R between the points of emission and reception of the signal according to the time of its propagation between these points. In radio navigation, rangefinders operate with an active response signal emitted by the transponder transmitter antenna (Fig. I.5.1) when receiving a request signal. If the propagation time of the request signals t 3 and answers t O is the same, and the time of formation of the response signal in the transponder is negligible, then the range measured by the interrogator (radio rangefinder)

The reflected signal can also be used as a response, which is what is done when measuring the radar range or altitude with a radio altimeter.

The position surface of the rangefinder system is the surface of a ball with a radius R. The position lines on a fixed plane or sphere (for example, on the surface of the Earth) will be circles, which is why rangefinder systems are sometimes called circular . In this case, the location of the object is determined as the point of intersection of two position lines. Since the circles intersect at two points (Fig. 2.3), ambiguity of reference arises, to eliminate which additional means of orientation are used, the accuracy of which may be low, but sufficient for a reliable choice of one of the two intersection points. Since the signal delay time can be measured with small errors, rangefinder RNS make it possible to find coordinates with high accuracy. In turn, rangefinder systems are divided into

Radio range finders without transponder;

radio range finders with transponder;

radio altimeters.

Principle of operation radio range finder without transponder lies in the fact that when measuring the distance between a reference point on Earth and an object (target), the time interval between the moment a radio pulse is sent by a ground-based radio transmitter and the moment it is received by an on-board radio is measured. To do this, there must be time standards on board and on the ground that synchronize the operation of ground and on-board equipment. The parameter of a radio rangefinder without a transponder will be distance between the requester and the object (target).

In radio rangefinders with transponder The time interval between the request and response radio pulses is measured. The parameter of such a radio range finder will be double the distance between the interrogator and the responder.

Parameter radio altimeter is twice the height of the aircraft above the ground.

Radio range finding methods began to be used later than goniometric methods. The first samples of radio range finders based on phase measurements of time delay were developed in the USSR under the leadership of L. I. Mandelstam, N. D. Papaleksi and E. Ya. Shchegolev in 1935-1937. The pulse range measurement method was used in the pulse radar developed in 1936-1937. under the leadership of Yu. B. Kobzarev.

Difference-rangefinder method.

Using a receiver indicator located on board the object, the difference in the time of reception of signals from the transmitters of two reference stations is determined: A And IN. station A called the master, since with the help of its signals the work of the slave station is synchronized IN. Measuring the distance difference proportional to the time shift of signals from the station A and B, allows us to find only the position surface corresponding to this difference and having the shape of a hyperboloid. If the receiver indicator and stations A And IN located on the surface of the Earth, then the measurement
allows you to obtain a line of position on the earth's surface in the form of a hyperbola with
. For two stations, you can construct a family of hyperbolas with foci at the points where the stations are located A and B. The distance between stations is called base . For a given base, a family of hyperbolas is mapped in advance and digitized. However, one pair of stations allows one to determine only the position line on which the object is located. To find its location, a second pair of stations is needed (Fig. II.2.3), the base of which d 2 should be located at an angle to the base d 1 first pair. Usually the leading station A is common and synchronizes the operation of both slave stations IN 1 And IN 2 . The grid of position lines of such a system is formed by two families of intersecting hyperbolas, which make it possible to find the location of the object (target) using the receiver indicator (RI) located on board. The accuracy of the difference-rangefinder system is higher than the goniometric accuracy and approaches the rangefinder accuracy. The advantage of this method is the unlimited number of throughput, since ground stations can serve an unlimited number of PIs located within the range of the system, since there is no need to have a transmitter on board the detected object, as in a rangefinder system. It should be noted that the asymptotes of hyperbolas are straight lines passing through the center of the base of each pair of stations in the system. Thus, at distances several times greater than the length of the base, the position lines degenerate into straight lines, as a result of which the difference-rangefinder system can be used as a goniometer.

Depending on the types of signals from ground stations and the method of measuring the time shift of received PI signals, the following are distinguished:

pulse;

• pulse-phase difference-rangefinder RNS.

The principle of a pulsed difference rangefinder system was proposed by the Soviet engineer E.M. Rubchinsky in 1938, but such systems became widespread only towards the end of the Second World War, when methods for accurately measuring the temporal position of pulses were developed. The first phase difference-rangefinder system (phase probe) was created in the USSR in 1938. Later, this principle was used in the Decca, Coordinator, etc. systems.

Exist three main methods determining the spatial coordinates of objects:

lines and surfaces of position;

correlation-extreme;

dead reckoning.

But the last two are currently only applicable for autonomous navigation systems, i.e. when determining the location on the aircraft itself. Determination of target coordinates is currently based on the application of the method of lines and position surfaces.

The commonality of the physical foundations of radio ranging and radio direction finding is also expressed in the fact that the location of a target can be determined not only by its range and angles measured from one point O (Fig. 1.3), but also by measuring the range or angles from spaced reference points and,( Fig. 1.7). The most widely used rangefinder, difference

rangefinder, goniometer (direction finding) and rangefinder-goniometer

(combined) methods for determining target location.

Rice. 1.7. Methods for determining the location of objects:

a – rangefinder; b – difference-rangefinder; c – direction finding (angle-

lomeric)

In radar, to determine the location of a target (object), the positional method is most often used, based on the use of surfaces or position lines to determine the location of the object in space or on the surface of the Earth. The position surface is a geometric locus of points in space that meet the condition of constant parameter (measured coordinate relative to the reference point (range, angle, etc.)).

The location of the aircraft in space is found as the point of intersection of three position surfaces (PP). The intersection of two position surfaces gives a line of position (LP), which is the locus of points with constant values ​​of two parameters. To define a point in space, the intersection of three position surfaces or a line and a position surface is required. If the target and reference points are located in the same plane, two LPs are sufficient (determining the two-coordinates of the target, which are measured by two RLUs) (Fig. 1.7).

Rangefinder method is to determine the location of the target M

(Fig. 1.7, a) by measuring the distances between the target and support points ,.

Each position surface is a sphere centered at the support

at a certain point and with a radius equal to the range. Since the points M, ,are in the same plane, then the position surfaces transform into circles with radii and intersection point on the target M. There is one more point of intersection of the circles, but the ambiguity of measurements can be eliminated.

Difference-rangefinder method(Fig. 1.7, b) requires the presence on the plane of two pairs of support points, and,. One of them is usually common

(). Each pair of stations is used to obtain LPs in the form of hyperbolas with focuses at reference points. These lines are constructed as geometric places

points with a constant difference in distance: oti; oti. The intersection point of the hyperbolas coincides with the target M.

Goniometer(direction finding) method is based on the use of directional properties of antennas. This method is implemented using a direction finder installed at object M and two radio beacons located at control points and (Fig. 1.7, c) with base b.

A direction finder is a radio receiving device with a directional antenna, and a radio beacon is a transmitting device with an omnidirectional antenna. The direction finder measures the azimuths of the lighthouse, and since LPs with constant bearings (= const, = const) are straight lines passing at angles to the south - north direction, they have one intersection point, which is the desired one, i.e. coincides with the target M.

Range finder and goniometer the method (Fig. 1.2, 1.3, 1.8) requires the use of only one station containing a radio range finder and a direction finder. From station point O, the range finder determines the slant range of the target, and the direction finder sets the direction to the target, i.e. its azimuth α and elevation angle β.

Target M is located at the intersection of the surface of the range finder position in the form of a ball of radius and the direction finder LP - in the form of a straight line with angular coordinates α and β passing through point O. This method is most typical for radar, and the remaining methods are for radio navigation. However, even in radar, the location of a target is sometimes determined from two or more points. For example, if a conventional radar produces direction finding with large errors, then they resort to the rangefinding method, and if the rangefinder part of the radar cannot be used due to strong interference or due to the use of passive radar, then they resort to the direction finding method.

Rice. 1.8. PP when determining the location of an object by positional (far-

number-direction-finding) method

Thus, in radar, positional methods based on the use of PP or LP are used to determine the location of an object. The choice of method determines the number of RLUs included in the system.

Conclusion

1. Radar signals reflected from targets contain all the information about them, since when reflected, all signal parameters change (amplitude, frequency, initial phase, duration, spectrum, polarization, etc.).

2. Modern radar uses local and global signals. Local SCs are divided into cylindrical and spherical SCs, global SCs into geographical and geospherical SCs.

3. According to the principles of the formation of radar signals, radar methods are divided into active, semi-active and passive. In practice, they are often combined when designing radar systems.

4. In radar, positional methods based on the use of PP or LP are used to determine the location of an object.

The choice of method determines the number of RLUs included in the system.

Control questions:

1. The principle of measuring range in radar.

2. The principle of direction finding in radar.

3. The principle of speed measurement in radar.

4. The main elements of a spherical SC used in radar.

5. The main elements of a cylindrical SC used in radar.

6. Basic elements of geographical SC.

7. Basic elements of geocentric SC.

8. The essence of active methods for generating a radar signal.

9. The essence of semi-active and passive methods of generating a radar signal.

10. The essence of rangefinder and difference-rangefinder methods for determining the location of an object.

11. The essence of goniometer and rangefinder-goniometer methods for determining the location of an object.

Self-study assignment:

1. Study the lecture materials.

2. Prepare for the test using test questions.

Literature:

1. Bakulev P.A. Radar systems: Textbook for universities. –

M.: Radio engineering, 2004.

2. Belotserkovsky G.B. Radar Basics and Radar

devices. – M.: Soviet radio, 1975.

Radiotechnical methods of external trajectory measurements

Equipment for external trajectory measurements, based on the radio engineering principle, has a greater tracking range and is more universal compared to optical equipment. It allows you to determine not only the angular coordinates of the aircraft, but also the distance to the object, its speed, direction cosines of the range line, etc.

Ranging in radio engineering systems comes down to determining the delay time t D arrival of emitted or reflected radio signals that are proportional to the range

D=ct D ,

Where With=3×10 8 m/s - speed of propagation of radio waves.

Depending on the type of signal used, the definition t D can be carried out by measuring the phase, frequency or direct time shift relative to the reference signal. The greatest practical application has been found pulse (temporary) And phase methods. In each of them, range measurement can be carried out as unsolicited, so request way. In the first case, the range D=ct D, in the second - D=0.5ct D .

At request-free pulse method High-precision timers are installed on board the aircraft and on the ground x 1 And x 2, synchronized before launch (Fig. 9.5). According to impulses u 1 chronicler x 1 onboard transmitter P emits pulse signals with a period T. Ground receiving device Etc accepts them through t D =D/c. Interval t D between pulses of the ground chronicizer u 2 and impulses u 1 at the receiver output corresponds to the measured range.

At request pulse method the signal is sent by a ground transmitter, received by an onboard receiver and relayed back.

Rice. 9.5. The principle of range measurement using a pulse-free method.

The accuracy of these methods increases with increasing pulse frequency.

Phase method range measurement is that the signal delay is determined by the phase shift between the request and response signal (Fig. 9.6).

Rice. 9.6. Phase ranging method

The ground transmitter emits vibrations:

u 1 =A 1 sin(w 0 t+j 0)=A 1 sinj 1 ,

Where A 1- amplitude,

w 0- circular frequency,

j 0- initial phase,

j 1 - signal oscillation phase.

On-board equipment relays the signal u 1, and the ground receiver receives the signal

u 2 =A 2 sin=A 2 sinj 2 ,

Where j A- phase shift caused by the passage of a signal in the equipment, determined by calculation or experiment.

Changing the phase of signal oscillations u 2 relatively u 1 is determined by the relation:

j D =j 2 -j 1 =w 0 t D =LpD/(T 0 s),

where is the range from?

Where l 0- wavelength.

When measuring angular motion parameters Amplitude and phase methods are most widely used in aircraft radio engineering.

Amplitude method is based on a comparison of signal amplitudes at different positions of the transmitting or receiving antenna. In this case, two options for implementing goniometric systems are possible: amplitude direction finders and beacons. In the first case, the transmitting device P is located on the aircraft, and the radiation pattern of the ground receiving device Etc periodically occupies position I or II (Fig. 9.7).

Rice. 9.7. Amplitude method for measuring angular parameters

If the angle a=0, then the signal level at both positions of the radiation pattern will be the same. If a¹0, then the amplitudes of the signals will be different, and from their difference the angular position of the aircraft can be calculated.

In the case when information about the angular position must be located on board the aircraft, use amplitude beacon. To do this, a transmitter is installed on the ground, and the radiation pattern of the ground antenna is scanned, periodically occupying positions I and II. By comparing the amplitudes of the signals received by the onboard receiver, the angular position of the aircraft is determined.

Phase method based on measuring the difference in distances from the aircraft to two reference points O 1 And O 2(Fig. 9.8).

Rice. 9.8. Phase method for determining angular parameters

In this case, the distance to the object R 1 And R 2 determined by phase difference DJ harmonic oscillations emitted by a source located at points O 1 And O 2. Cosine of direction angle q defined:

Where IN- distance between points O 1 And O 2.

An example of a complex of external trajectory measurements used in field practice is the “Track” system (Fig. 9.10). This equipment, developed and produced by the SKB measuring equipment NTIIM, uses the coordinate-goniometer-basic principle.

It consists of two tracking television theodolites 1, a control system 2, a unified time synchronization system 3, a recording and information processing system 4. The “Track” system allows you to obtain information about coordinates, speed, drag coefficient, and also observe the behavior of an object on the monitor screen .

Rice. 9.10. System of external trajectory measurements “Track”:

1-tracking television theodolite; 2-control system; 3-unit time synchronization system; 4-systems for recording and processing information

The main characteristics of the “Track” system are given below:

Error in measuring angular coordinates at an elevation angle of up to 60 degrees:

Static - 15 arcsec

In dynamics - 30 arcsec,

Maximum object tracking parameters

Angular speed - 50 degrees/sec,

Angular acceleration - 50 degrees/sec 2,

The frequency of recording the angular coordinates of object images is 25-50 frames/sec.

The most important task of external ballistic research is to determine the spatial location of the aircraft’s center of mass, which is uniquely determined by three spatial coordinates. In this case, navigation uses the concepts of surfaces and position lines.

Under position surface understand the geometric location of the aircraft's location points in space, characterized by a constant value of the measured navigation parameter (for example, elevation angle, azimuth angle, range, etc.). Under position line, understand the intersection of two position surfaces.

The position of a point in space can be determined by the intersection of two position lines, three position surfaces, and a position line with a position surface.

In accordance with the type of measured parameters, the following five methods for determining the location of an aircraft are distinguished: goniometer, rangefinder, total and difference-rangefinder and combined.

Goniometer method is based on the simultaneous measurement of aircraft sighting angles from two different points. It can be based on both optical and radio engineering principles.

At cinetheodolite method application surface at a=const is a vertical plane, and the position surface at b=const- a circular cone with its apex at point O (Fig. 9.11, a).

Rice. 9.11. Determination of object coordinates using the film theodolite method,

a) surface and position line, b) coordinate determination scheme

Their intersection determines the line of position coinciding with the generatrix of the cone. Therefore, to determine the location of the aircraft, it is necessary to determine the coordinates of the point of intersection of two position lines OF 1 And OF 2(Fig. 9.11, b), obtained simultaneously from two measuring points O 1 And O 2.

In accordance with the scheme under consideration, the coordinates of the aircraft are determined by the formulas:

Where IN- distance between measuring points,

R- radius of the Earth in a given area.

Using rangefinder method aircraft coordinates are determined by the intersection point of three spherical position surfaces with radii equal to the range D. However, in this case, uncertainty arises due to the fact that the three spheres have two points of intersection, to eliminate which additional orientation methods are used.

Difference and total rangefinder method is based on determining the difference or sum of ranges from the aircraft to two measuring points. In the first case, the position surface is a two-sheet hyperboloid and to determine the coordinates of the object it is necessary to have one more (leading) station. In the second case, the position surface has the form of an ellipsoid.

Combined method Typically used in radar systems, where the aircraft's position is defined as the point of intersection of a spherical position surface with a radius equal to the range ( D=const), conical surface position ( b=const) and vertical surface position ( a=const).

Doppler method determining the speed and location of an aircraft is based on the effect of changing the frequency of the carrier signal emitted by the transmitter and perceived by the receiving device depending on the speed of their relative movement:

F d =¦ pr -¦ 0,

Where F d- Doppler frequency,

¦ pr - frequency of the received signal,

¦ 0 - frequency of the transmitted signal.

Doppler frequency measurements can be taken unsolicited or request method. At unsolicited method, the radial speed of the aircraft at the signal wavelength l 0, is defined:

V r =F d l 0,

at request method:

V r =F d l 0 /2.

To determine the range, you must integrate the results of measuring the flight speed over the time the object moves from the starting point. When calculating coordinates, dependencies for total rangefinder systems are used.

Schemes for determining aircraft parameters based on the Doppler effect are shown in Figure 9.12.

Rice. 9.12. Scheme for determining aircraft coordinates using the Doppler method:

a) without signal relay, b) with signal relay

When carrying out external trajectory measurements of the movement of small aircraft (bullets, artillery and rocket shells), Doppler range radar stations DS 104, DS 204, DS 304 manufactured by NTIIM are used.

Rice. 9.13. Doppler range radar stations

DS 104, DS 204, DS 304

They use the query method and allow you to determine speeds on any part of the trajectory, current coordinates in the vertical plane, calculate accelerations, Mach numbers, drag coefficient, average and median deviations of the initial speed in a group of shots.

The main technical characteristics of the DS 304 station are as follows:

Minimum caliber - 5mm,

Speed ​​range - 50 – 2000 m/s,

Range - 50000 m,

Speed ​​measurement error - 0.1%,

Probing signal frequency - 10.5 GHz,

The level of generated signal power is 400 mW.