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ENCYCLOPEDIA OF RADIO ELECTRONICS AND ELECTRICAL ENGINEERING Geotronics: electronics in geodesy. Encyclopedia of radio electronics and electrical engineering
Encyclopedia of radio electronics and electrical engineering / Beginner radio amateur
Geodetic measurements on the earth's surface solve many problems. First of all, this is the creation of maps of various scales. But not only: geodesy, together with astronomy, gravimetry (the science of measuring the acceleration of gravity), geophysics and other Earth sciences, allows you to determine the geometric and geophysical parameters of the planet, study variations in its rotation speed, take into account the movement of the poles, study deformations of the earth's crust, and carry out precision control of engineering structures. Marine geodesy, applied geodesy, space (satellite) geodesy, etc. have emerged as separate areas. But in all cases, geodetic measurements themselves are reduced to determining only three geometric quantities: distances, angles, and elevations (differences in point heights). These quantities can be useful on their own, especially in applied geodesy (on construction sites, when marking the terrain), but, most importantly, they allow you to calculate the coordinates of the points being determined. Coordinates are of interest not only to surveyors - they are needed by sailors, aviators, the military, members of various expeditions, and many more. If we go back half a century ago, we will find the following picture. Distances are measured with steel 20-meter tapes, successively laying them on the ground along the measured line, and for accurate measurements - with suspended 24-meter invar wires. (It was extremely time-consuming work!) For fast measurements, optical rangefinders are used, based on the use of a purely geometric principle - the solution of a highly elongated ("parallactic") triangle with a small base (base), but the accuracy of such rangefinders does not exceed one thousandth of the length of the measured lines, and the range is several hundred meters. For angular measurements, theodolites are used - optical-mechanical goniometers containing a telescope, horizontal and vertical goniometric circles and reading devices for measuring angles. Finally, to determine the excesses, levels are used, which are a combination of a telescope with an accurate bubble level, which allows you to bring the sighting axis of the pipe to a strictly horizontal position. After bringing the observer takes readings on two rails with divisions, vertically installed on the points, the difference in heights of which must be determined; the difference between the readings and gives the desired excess. Thus, all geodetic instruments of that time were exclusively optical-mechanical instruments. The situation persisted until about the mid-50s. And then came a period that can be safely called a revolution in geodetic instrumentation: electronics came to geodesy. It began its triumphant march with linear measurements, then penetrated into angular measurements, and more recently into the most conservative area - leveling. A huge role was played by the appearance of lasers in 1960, the development of microelectronics, and later - computer technology and satellite technologies. The merging of geodesy and electronics led to the formation of a new concept - geotronics. What is geotronics today? First of all, electromagnetic waves are used to measure distances instead of measuring tapes and wires, which reduced the time of actual measurements (that is, not counting the time for installing devices) to literally a few seconds (instead of days and weeks!), and regardless of the length of the measured line . There are two main approaches here. The first is that the distance between, say, points A and B is obtained by measuring the propagation time of electromagnetic waves from A to B and multiplying it by the propagation velocity v. (The latter can be found as c/n, where c is the speed of light in vacuum, known very accurately, an is the refractive index of air, calculated from measurements of temperature, pressure, and humidity). This way is especially convenient when using electromagnetic radiation (in particular, light) in the form of short pulses. The propagation time τ is measured as follows: a pulse emitted from point A triggers an electronic time counter. Having traveled the distance to point B and back (a reflector is located at point B), the impulse stops the counter. Thus, double propagation time is measured. The method is called time or impulse and, in fact, differs little from impulse radar, although it is used, as a rule, in the optical range. The second approach to measuring distances is very similar to the situation with measuring tapes: as a kind of measuring tape, the wavelength of the electromagnetic oscillation (with continuous radiation) acts, which is "laid" in the double measured distance and the number of layings is determined. The distance is obtained as half the product of the wavelength and the number of positions. This number in the general case (as well as when measuring with a tape) will not be an integer - it is equal to N + ΔN, where N is an integer, and ΔN is a fraction less than one. The wavelength can be determined by knowing in advance or by measuring the oscillation frequency. The fractional part of ΔN is easy to obtain, for this you need to measure the phase difference of the emitted and received (passed double distance) oscillations. But the definition of an integer N is the main problem. It can be solved by measuring the phase difference at several different wavelengths. Since phase differences are measured, this method is called phase. In terrestrial phase light and radio rangefinders, measurements are made using not the radiation wavelength, but the modulation wavelength, which is much longer. The fact is that the frequency of the radiation itself is too high to determine the phase. A generalized scheme for constructing a phase rangefinder is shown in fig. 1.
A source of light or radio waves emits carrier harmonic oscillations of the form Asin(ωt + φo). But before radiation, one of these parameters (in light range finders, usually the amplitude A, which determines the light intensity, and in radio range finders, the frequency f = ω / 2π) is modulated according to a sinusoidal law with a certain frequency F, much lower than the carrier frequency f. This frequency corresponds to longer "waves of modulation", which play the role of a measuring tape placed in the measured distance. In this case, the fractional part of the regulations ΔN = Δφ/2π, where the phase difference Δph, which lies in the range from 0 to 2π, is measured by a phase meter. Ground-based phase rangefinders measure distances up to several tens of kilometers with an error of several centimeters to several millimeters. The pulse method is used in geodesy, as a rule, in the optical wavelength range with powerful laser radiation sources that generate optical pulses in the visible or, more often, near infrared region of the spectrum. However, due to the difficulty of forming short pulses with a steep front, the accuracy of this method is lower than that of the phase method - at best, decimeters. Therefore, pulsed laser ranging systems are used to measure very large distances on space paths (to artificial satellites of the Earth and even to the Moon), where, due to the large length of the path, the relative error is very small. For short distances (tens and hundreds of meters), the most accurate is the optical interference method, which makes it possible to measure these distances with an accuracy unattainable by any other methods - up to thousandths of a millimeter (micrometers). It is implemented using laser interferometers with a low-power helium-neon (He-Ne) laser emitting in the red region of the spectrum at a wavelength of λ = 0,63 μm. The interferometer is built according to the well-known Michelson scheme in optics: the laser radiation is divided into two beams, one of which, with the help of a "reference" reflector, is directed immediately to the photodetector, and the other arrives at the same photodetector after passing the distance to the "remote" reflector and back. An interference pattern is formed on the photodetector in the form of a system of dark and light bands, of which only one band can be distinguished using a diaphragm. The method requires moving a distance reflector along the entire measured line. When the reflector is moved by half the wavelength of light, the interference pattern is shifted by one fringe, and by counting the fringes when the reflector is moved from the start to the end point of the measured distance, this distance is obtained, as in phase rangefinders, by multiplying the number of counted fringes (number N) by λ/2. For a movable reflector, it is necessary to build carefully adjusted rail guides, rigidly fixed on strong concrete supports. Therefore, the scope of laser interference measurements is the creation of stationary multi-section bases for metrological purposes for calibrating electronic geodetic rangefinders. Advances in radio astronomy made it possible to create a very long baseline radio interferometer (VLBI). It consists of two radio telescopes 1 and 2 separated by a very large distance (up to thousands of kilometers) (Fig. 2), which receive noise radiation from the same quasar - an extragalactic radio source.
Radio telescopes independently record (on video recorders) this noise signal. Both records are identical, but shifted in time by a value due to the difference in distances from the quasar to the radio telescopes. The records are combined in a correlator, which makes it possible to obtain the correlation function of the noise signals. If one of them is written as s1(t) and the other as s2(t + τ), then the correlation function K12 = , where angle brackets mean averaging over a time much greater than the period of the lowest frequency component of the signals s1 and s2. The correlation function has a maximum at τ = 1. Therefore, by shifting one of the records until the maximum output signal is obtained at the output of the correlator, one can measure the time delay. Since, due to the Earth's rotation, the difference ΔS of the distances to the quasar, and hence the delay m = ΔS/v, changes periodically, an "interference frequency" F occurs, which can also be measured. The measured values of τ and F are used to determine the length of the base (the distance between radio telescopes) and the direction to the quasar with very high accuracy (2...0 cm and 2" respectively). Electronics made it possible to automate angular measurements as well. An electronic theodolite is a device that converts angular quantities recorded as a system of opaque strokes or code tracks on a glass disk into electrical signals. The disc is illuminated by a light beam, and when the theodolite is rotated on the photodetector, a signal is generated in binary code, which, after decoding, provides an indication of the angular value in digital form on the display. Combining an electronic theodolite, a small-sized phase light rangefinder and a microcomputer into a single integral or modular design made it possible to create an electronic total station - a device that allows you to perform both angular and linear measurements with the possibility of their joint processing in the field. The accuracy of such instruments ranges for angular measurements from a few arcseconds to 0,5", for linear measurements - from (5mm + 5mm / km) to (2mm + 2mm / km), and the range is up to 2 ... 5 km. Finally, let us briefly mention progress in leveling work. The introduction of laser technology into geodesy has led, in particular, to the development of the "laser plane" leveling method (Laserplane systems). A bright red beam of a vertically located He-Ne laser falls on a rotating prism, which creates a beam sweep in a horizontal plane. This allows you to take a reading from the light spot on the rail placed in any direction from the laser. Photoelectric indication provides reading accuracy of the order of 1 mm. The method is fast and does not limit the number of rails, which is convenient for many high-altitude surveys. For accurate leveling, a digital level is currently designed that works on a coded rail. The code carries information about the height of any place on the rail relative to its "zero". The image is converted into an electrical signal, and when working on two rails, the excess between the points of their installation is automatically determined. Let us also mention the wide application of the He-Ne laser in applied geodesy, due to the fact that the laser beam is a physically realized and almost perfectly straight reference line in space, relative to which measurements are taken during precise installation of equipment, construction, etc. Over the past 20 years, a new qualitative leap has taken place in geotronics, which is called the second revolution in geodetic measurements. This is the creation of global satellite navigation and geodetic systems. They implement fundamentally new measurement methods, which we will discuss in the second part of our article. The advent of global satellite systems made it possible to determine the coordinates at any point on the Earth at any time. At the same time, reference is made to the reference time scales, and for a moving object, its velocity vector (speed and direction of motion) is determined. All this, taken together, is often referred to as "satellite positioning". Currently, there are two global systems in the world: the American GPS (Global Positioning System) and the domestic GLONASS (Global Navigation Satellite System). These are ranging-type systems that calculate the coordinates of a ground-based receiver from measurements of distances to moving satellites, the instantaneous coordinates of which are known as a result of the operation of the ground-based complex. The receiver location is obtained at the intersection of all measured distances (linear intersection). In contrast to terrestrial ranging, where the signal travels the measured distance twice - in the forward and backward directions, satellite systems use an unsolicited method with a single passage of the signal along the path. The signal is emitted from the satellite and received by a ground receiver, which determines the propagation time τ. The distance between the satellite and the receiver p = vτ, where v is the average speed of signal propagation. Let the satellite emit a signal at time t0, and this signal arrives at the receiver at time t0 + τ, and we need to determine m. To do this, the satellite and the receiver must have clocks that are strictly synchronized with each other. The satellite signal contains a timestamp transmitted every few seconds. The label "records" the moment of its departure from the satellite, determined by the clock of the satellite. The receiver "reads" the timestamp and fixes the moment of its arrival according to its clock. The difference between the moments when the tag leaves the satellite and arrives at the receiver antenna is the desired time interval τ. In fact, clock synchronization is not respected. The satellite sets the frequency standards (and hence the time) with a relative instability of 10-12...10-13. It is impossible to have such standards in each receiver; they put ordinary quartz clocks with an instability of the order of 10-8 there. An unknown value Δh appears - the difference between the clock readings of the satellite and the receiver, which distorts the result of determining the range. For this reason, the ranges obtained from measurements are called pseudoranges. How they determine the coordinates, we will describe below. The GPS and GLONASS systems consist of three sectors (Fig. 3).
A space sector is a collection of satellite systems, often referred to as a "constellation" or "orbital constellation". A complete constellation consists of 24 satellites. In GPS they are located in six orbital planes rotated through 60°, and in GLONASS - in three planes through 120°. Almost all circular orbits have an altitude of about 20 km, the period of revolution is close to 000 hours. The command and control sector includes tracking stations, an exact time service, a main station with a computer center, and stations for downloading information to satellites. Tracking stations determine the ephemeris (orbital elements) of the satellites and calculate their coordinates. The information is transmitted to the satellites by the loading stations and then broadcast to the receivers. The user sector is satellite receivers, the number of which is not limited, and a cameral complex for processing measurements ("post-processing" performed after field observations). satellite signal. Signals are emitted from the satellite on two carrier frequencies L1 and L2. They are subjected to phase shift keying (PM) - transfer of the carrier phase by 180 ° at times specified by ranging binary codes. A phase reversal corresponds to a change in codes 0 to 1 or 1 to 0. Rangefinding codes are such an alternation of characters (zeros and ones) that it is impossible to notice any patterns in it, but after some time intervals they are periodically repeated with an accuracy of each character. Such processes are called pseudo-random sequences (PRS) - they form pseudo-random codes. Two codes are used: one for "rough", the other for "fine" measurements. They have a significantly different repetition period (code duration). So, in GPS, a rough code, called the C / A code (from the words Coarse Aquisition - easily detectable, publicly available), is repeated every millisecond, and the duration of the exact code, called the P-code (Precision - exact), is 266,4 days. The total duration of the P-code is divided into weekly segments distributed over all satellites of the system, i.e., the P-code of each satellite changes every week. While the C/A code is available to all users, the P code was originally intended only for those with authorized access (mainly the US military). Now, however, the receivers of almost all users have access to the R-code. In the GLONASS system, the situation is similar, the difference is only in the names: the rough code is called the ST code (standard accuracy), and the exact code is called the BT code (high accuracy). However, there is a fundamental difference between GPS and GLONASS related to the use of codes. In GPS, both the C/A code and the P code are different for each satellite with the same carrier frequencies L1 and L2, while in GLONASS, on the contrary, the ST and BT codes of all satellites are the same, but the carrier frequencies are different. In other words, GPS uses code separation, while GLONASS uses frequency separation of satellite signals. The rough code is manipulated by the L1 carrier, and the fine code is manipulated by both the L1 and L2 carriers. The satellite signal also "embeds" all the information transmitted from the satellite, forming a navigation message - timestamps, data on the satellite's ephemeris, various correction values, almanacs (a collection of data on the location of each of the satellites of the system and the state of its "health"), etc. It is also converted to binary code, which is manipulated by both carriers. The frequency of the symbols of the navigation message is 50 Hz. The general scheme of formation of a satellite signal in GPS is shown in fig. 4.
Modern satellite receivers can operate in two main modes, called code and phase measurements. Code measurements are also called absolute, since they allow you to directly determine the coordinates of points X, Y, Z in a geocentric (i.e., with the origin at the center of mass of the Earth) rectangular coordinate system, and the mode of code measurements is called navigation. In code measurements, the propagation time of the PM signal from the satellite to the receiver is determined, including the delay in the atmosphere and the relative clock correction Δtch. The measurements are carried out by the correlation method. In the receiver, exactly the same PSS is formed as on the satellite. This local code and the signal received from the satellite are fed to a correlator that reverses the phase of the signal by 180° when the local code symbols change. The delay of the local code relative to the satellite is forced to change until the codes completely match. At this moment, the manipulation is removed at the output of the correlator and the signal power sharply increases (which corresponds to the maximum of the correlation function). The required delay corresponds to the propagation time of the signal. In this way, the delay can only be measured within the duration of the code (its repetition period), which for a coarse code is 1ms. The propagation time tr that interests us is much longer. In 1 ms, a radio wave travels 300 km, and the number of whole milliseconds in the propagation time is determined by the approximate value of the distance, which must be known to within 150 km. When using the exact code, this problem does not arise, since its duration is greater than the propagation time τр. Having determined τр and multiplying it by the speed of light in vacuum, one obtains the pseudorange Р, related to the geometric range р by the relation Р = р + cΔtaтм + cΔtch, where cΔtaтм is the signal delay in the atmosphere (which can be determined with varying degrees of accuracy); c is the speed of light in vacuum. In this ratio, the unknowns are p and Δtch. But the geometric distance p between the satellite and the receiver can be expressed in terms of their coordinates. Since the satellite coordinates are known from the navigation message, p contains three unknown receiver coordinates X, Y, Z, and the equation for P actually contains four unknowns - X, Y, Z and At, . By simultaneously measuring up to four satellites, a system of four equations with four unknowns is obtained, from the solution of which the desired coordinates of the receiver are found. Simultaneity is necessary to maintain the constancy of the value of Δtch. The accuracy of code measurements is significantly increased by using a differential method using two receivers, one of which (base) is installed at a point with known coordinates and continuously operates in the P-code. The pseudo-ranges measured by him are compared with the "reference" ones calculated from the coordinates. The resulting differences, or differential corrections, are sent to the rover to correct the measurements. The differential method gives an accuracy of up to several decimeters. Phase measurements are performed with two receivers and are relative measurements, in which not the coordinates of the receivers themselves are determined, but the differences of their coordinates of the same name. The phase measurement mode is called geodetic because it provides much better accuracy than the code measurement navigation mode. In this case, it is not the signal propagation time from the satellite to the receiver that is measured, but the phase shift of the carrier frequency oscillations during this time. However, from the measurements, we can obtain not the total phase shift φSR = 2 N + Δφ, "progressing" at a distance from the satellite S to the receiver R, but only its fractional part Δφ, less than 2π. The unknown number of complete phase cycles N is the number of integer wavelengths that fit within the distance from the satellite to the receiver. Since the distance is large (20 km) and the wavelength is small (000 cm), N is on the order of 20 million, and it must be determined exactly: an error per unit will give an error in range of 100 cm. Methods for solving this problem have been developed in which the main role is played by the mathematical processing of the measurement results, carried out by software. From phase measurements, phase pseudoranges are obtained, in which the value of Δtch has a slightly different interpretation. If during code measurements it reflects the non-synchronism of the satellite and receiver clocks, then during phase measurements it is a consequence of the non-synchronous oscillations of the reference oscillators of the satellite and the receiver, which we denote by bf. Of course, Δtch and δφ are rigidly related to each other: δφ = 2πf ·Δtch. To exclude δφ, it is sufficient to perform measurements on two satellites. The value of δφ can be represented as δφS - δφR (ie, the difference between the initial phases of the oscillations of the generators on the satellite and in the receiver). If observations of one satellite are performed simultaneously with two spaced receivers, the value δφS for the observed satellite is excluded from the difference of the results. If the same receivers observe the second satellite, the difference excludes the value of δφS for this second satellite. If we now make up the difference of differences - the so-called second difference, the value of δφR for both receivers is excluded. The second difference method is the main one for high-precision geodetic measurements. The second phase pseudo-range difference contains the coordinates of two satellites 1 and 2 and two receivers A and B. Let's denote it P12 . If we perform measurements of phase pseudoranges to four satellites at points A and B, we can compose three independent equations: for P12, P13 and P14, in which three differences of the same coordinates of points A and B will act as unknowns: (ХА - ХB), (YА - YB), (ZA - ZB). The solution of such a system of equations makes it possible to find the length of the base AB, and if one of the receivers is placed at a point with known coordinates (which they do), then the coordinates of the second point can be easily found from the obtained differences. To make phase measurements at carrier frequencies, it is necessary to free them from code modulation. This is achieved by squaring the signal coming from the satellite (multiplying by itself), as a result of which a 180 ° phase change turns into a 360 ° change, i.e. phase keying is removed and the carrier is restored (at twice the frequency). Phase measurements provide accuracy at the centimeter, and in some cases even at the millimeter level. The scope of the article does not allow highlighting many interesting details, but we hope that the reader has received a general idea of the achievements of the new modern science - geotronics. Author: A.N. Golubev, Doc. tech. sciences, prof. Moscow State University of Geodesy and Cartography
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It is difficult to name the area of human activity, which would not penetrate the achievements of modern radio electronics. Not left aside and one of the most ancient sciences - geodesy, the science of "measuring the Earth."
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