Where to get accurate GPS ephemeris from. The leading station updates the satellite ephemeris several times a day

After the statement by Deputy Prime Minister Dmitry Rogozin that Russia will suspend the operation of 11 ground stations from June 1 GPS on their territory and that, perhaps, from September 1, the work of these stations could be completely stopped, office hamsters were seriously alarmed. Now how will they find their way to the refrigerator without GPS? And will they be able to get to work if the navigator in the car doesn’t tell you where to turn?

Instead of understanding why these stations were needed at all, they began to literally sow panic on the Internet. After all, not all phones and navigators have GLONASS.

Today I will talk briefly about what base stations are used for GPS, and whether the world would really collapse without them.

First, let’s figure out why this commotion started. The Deputy Prime Minister’s statements and further actions are a symmetrical response of the Russian government to the US refusal to place signal correction stations for the Russian GLONASS navigation system on its territory. And any global navigation system, be it Russian GLONASS, American GPS, European GALILEO, or Chinese COMPASS were created primarily for military use (roughly speaking, to guide missiles more accurately), and various civilian applications are just a by-product. And in light of recent events in the political arena, such statements by our government are quite reasonable.

Everyone has probably seen videos in the news about ultra-precise weapons. Here are some statistics: in Operation Desert Storm, only about 10% of the military equipment used by the Americans used the system GPS for precise guidance, and already in the conflict in Kosovo, GPS was used in 95% of cases for the same purposes.

So what are ground stations for?

Receivers are installed at ground stations GPS for passive tracking of navigation signals from satellites included in the system. After receiving from the satellite, the information is transmitted, where it is subsequently processed at the main control station. This data is used to update satellite ephemeris.

An ephemeris is a table containing the coordinates of a celestial body, given at various times over a certain period. Astronomers and surveyors use ephemeris to determine the positions of celestial bodies, which are later taken to calculate the coordinates of points on the Earth's surface.

For us GPS ephemerides can be compared to GPS satellites, and imagine them as a constellation of artificial stars. To calculate our location relative to satellites GPS, we need to know their location in space, in other words, we need to know their ephemeris. There are two types of ephemeris: transmitted (on-board) and accurate.

Transmitted ephemeris

The transmitted ephemeris comes from GPS satellites. They contain information about Keplerian orbital elements that allow the GPS receiver to calculate the global geocentric coordinates of each satellite, relative to the original WGS-84 geodetic date (this is a three-dimensional coordinate system for positioning on Earth. In this system coordinates are determined relative to the Earth's center of mass. The reference date is the date when the center of mass was determined). Keplerian elements consist of information about the coordinates of satellites for a certain epoch and changes in orbital parameters from the reporting period to the moment of observation (the calculated rate of change of parameters is accepted). Ground stations constantly monitor the pre-predicted positions of satellite orbits, generating a stream of ephemeris information. Next, the main control station transmits the transmitted ephemeris to the satellites. The calculated accuracy of the transmitted ephemerides is about 2.5 m and about 7 ns.

Accurate ephemeris

Accurate ephemeris consists of the Earth-wide geocentric coordinates of each satellite as defined in the Earth-wide Reporting System and includes clock corrections. Ephemeris are calculated for each satellite at a certain interval. Accurate ephemeris is a post-processing product. Data is collected by ground stations and then transmitted to the International Service GPS, where the calculation of exact ephemerides takes place, which already have an accuracy of about 5 cm and 0.1 ns.

Disabling ground stations GPS can only affect the accuracy of positioning and it is unlikely that such accuracy is needed for our everyday tasks. The average person, I think, will not feel the potential decrease in this accuracy when using a smartphone as a navigator.

Despite the fact that the very fact of turning off base stations will not lead to the fact that devices using the system GPS will no longer determine coordinates, but will only potentially reduce them; a further step could theoretically be a decision by the US government to stop transmitting the signal GPS on the territory of the Russian Federation (American satellites simply flying over Russia will not broadcast the signal). Of course it's possible. But this has not happened yet, and is unlikely to happen tomorrow or in a week. And in six months, the smartphone in your pocket will no longer be fashionable and you will need to choose a new gadget. Then you will need to take a closer look at devices that have GLONASS and I think that in the near future their choice will only increase.

The accuracy that GLONASS provides today is somewhat lower than that of GPS, but this gap is narrowing with each new Russian satellite launched as part of the domestic program. In addition, it takes a little more time for the so-called “cold start” - the signal from the first satellite found in GLONASS devices is searched for a little longer from the user’s point of view, and, in fact, this is not so scary.

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The location accuracy of the navigation system is limited due to the influence of various factors. They can be divided into two groups. Errors in calculating the location of satellites and the influence of the atmosphere (troposphere and ionosphere) on the speed of the radio signal.

As already mentioned, navigation satellites play the role of radio beacons, transmitting signals of the exact time and their coordinates. It is worth noting that satellites do not know anything about their location. Their coordinates are determined by the control sector and, as a result, orbital characteristics - ephemerides - are calculated. These ephemeris (a set of numerical coefficients) are downloaded to a satellite, which transmits them along with the rest of the navigation information. A GPS receiver receives a signal from a satellite and calculates its coordinates using the resulting set of orbital coefficients. These coefficients (ephemeris) are updated by the leading station several times a day as needed. But nevertheless, the calculated coordinates are inaccurate. The satellite location is determined with an error. Why?

If the Earth had the shape of a sphere with a density uniform in depth and there were no other influences on the satellite, then it would move strictly along the same ellipse in accordance with Kepler’s First Law. But the shape of the Earth differs from a sphere, in addition, the Sun and Moon, as well as non-gravitational factors, act on the satellite. Therefore, the parameters of the ellipse are constantly changing. This leads to errors in calculations. Here is a table of various impacts on the satellite in descending order (A.L. Genike, G.G. Pobedinsky “Global satellite systems ...”, 2004):

Table 1. The influence of various disturbances on the movement of a navigation satellite

The first on the list is the central field of the Earth. Thanks to it, the satellite moves along an ellipse with an acceleration of 0.565 m/s 2 . This is the acceleration of free fall at an altitude of 20.2 thousand km. Gravity is always attraction, so the gravitational field does not have a first (dipole) correction. The second zonal harmonic comes immediately. It introduces a disturbance 10 thousand times less: 5.3×10 – 5 m/s 2 . As a result, in 1 hour the satellite can deviate by 300 meters from the calculated trajectory. And in 3 hours - already 2 km, since the error increases nonlinearly.

The gravitational influence of the Moon is an order of magnitude less, and the Sun’s is even 2 times less. Of the non-gravitational influences, solar radiation (solar wind) comes first. Gravity anomalies are caused by the uneven distribution of mass inside the Earth (see photo above). They deflect the satellite by 6 cm in an hour. Lunar and solar tides also contribute to the redistribution of masses on the Earth's surface. Despite their relative smallness, in two days they can deflect the satellite from the calculated orbit by 2 meters.

The management sector focuses on these data, but does not use them in its calculations. All ephemeris are calculated solely based on observations. When calculating orbital motion, it is generally accepted that the satellite moves strictly along an ellipse, as if there were no disturbances. This orbit is called osculating. After a short period of time, the orbital parameters change, and the satellite moves along a different ellipse. And so on. Thus, the entire effect of disturbances is reduced solely to a continuous change in the parameters of the osculating ellipse.

Thanks to numerous observations of the movement of satellites, the leading station selects a mathematical model that is capable of calculating this movement with the least errors. The model's numerical coefficients (ephemeris) are regularly updated and uploaded to the satellites three times a day. In addition, the ephemeris is updated every hour.

It is important to note that the navigation system is constantly evolving. The coordinates of the reference stations are being clarified. Using reference stations with more accurate coordinates, it is possible to more accurately determine the satellite's ephemeris, and so on.

However, modern errors in determining satellite ephemeris lead to errors in calculating their coordinates at the level of 10-20 meters. At first glance, this seems like a lot. This is true if you determine the location coordinates in an absolute (direct) way. But the navigation system uses a differential (relative) method for determining location (see here). Thanks to this method, it is possible to increase the accuracy of determining coordinates by a hundred times or more.

This accuracy is already sufficient even for most geodetic work. But, say, to study the movement of the earth's crust, even higher accuracy is required. In these cases, it is not the ephemeris transmitted over the satellite radio channel that is used, but their significantly refined values obtained as a result of subsequent observations. Long-term observations of satellite orbits make it possible to clarify ephemeris values in the past. These updated values are accumulated in a special bank operating in the USA under the National Geodetic Service (NGS).

What are ephemeris?

In the famous Webster's Dictionary of Definitions, the following definition of the term ephemeris is given: An ephemeris is a table of coordinates of a celestial body given at various times over a certain period. Astronomers and surveyors use ephemeris to determine the positions of celestial bodies, which are later taken to calculate the coordinates of points on the earth's surface.

In general, for us, GPS ephemeris can be compared to GPS satellites, and imagined as a constellation of artificial stars. In order to calculate our location relative to GPS satellites, we need to know their location in space, in other words their ephemeris. There are two types of ephemeris: transmitted (on-board) and accurate.

Transmitted (on-board) ephemeris

Transmitted (on-board) ephemeris, as their name suggests, is transmitted directly from GPS satellites. The transmitted ephemeris contains information about Keplerian orbital elements that allow the GPS receiver to calculate the global geocentric coordinates of each satellite, relative to the original WGS-84 geodetic date. These Keplerian elements consist of information about the coordinates of satellites for a certain epoch and changes in orbital parameters from the reporting period to the moment of observation (the calculated rate of change of parameters is accepted). Five monitoring stations constantly monitor the pre-predicted positions of the satellites' orbits, generating a stream of ephemeris information. Next, the Navstar main control station transmits the transmitted ephemeris to the satellites daily. The calculated accuracy of the transmitted ephemerides is ~260 cm and ~7 ns.

Accurate ephemeris (Final products)

Accurate ephemeris consists of the Earth-wide geocentric coordinates of each satellite as defined in the Earth-wide Reporting System and includes clock corrections. Ephemeris are calculated for each satellite at 15 min intervals. Accurate ephemeris is a post-processing product. Data is collected by tracking stations located throughout the Earth. This data is then transmitted to the International GPS Service (IGS), where the exact ephemeris is calculated. Accurate ephemeris becomes available approximately 2 weeks after the time of data collection and has an accuracy of less than 5 cm and 0.1 ns.

The exact ephemeris can be downloaded from the NASA server:
ftp://igscb.jpl.nasa.gov/igscb/product/

Rapid ephemeris (Rapid products)

Fast ephemeris is calculated in the same way as accurate ephemeris, but the processing uses a smaller data set. Fast orbits, as a rule, are “posted” to the services of international agencies the next day. The accuracy of fast ephemeris is 5 cm and 0.2 ns.

Fast ephemeris can be downloaded from the IGS server:
http://igscb.jpl.nasa.gov/components/dcnav/igscb_product_wwww.html

Predicted or Ultrafast ephemeris (Ultrarapid products)

Ultrafast ephemeris are transmitted like transmitted ephemeris, but they are updated twice a day. They are sometimes called real-time ephemeris. This can be explained by the fact that they are used in the same way as transmitted ephemeris, but for real-time applications. The accuracy of ultrafast ephemeris is ~25 cm and ~5 ns.

Ultrafast ephemeris can be downloaded from the IGS server:
http://igscb.jpl.nasa.gov/components/dcnav/igscb_product_wwww.html

Do we need accurate ephemeris?

To answer this question, let's establish a relationship between the accuracy of the ephemeris and the accuracy of the GPS vector solution. Let's assume we are talking about a 10 km long baseline. We process the line using the transmitted ephemeris (accuracy 2.60 m). In this case, the expected accuracy will be (10 km /20000 km) * 2.60m = 1.3 mm. If the length of the baseline is 100 km, the error will increase to 13 mm. These figures allow us to conclude that on short baselines (up to 100 km) the use of transmitted ephemerides is more than sufficient.

In general, we can say that due to the development of the GPS system, the need for accurate ephemeris has decreased somewhat. For example, just a few years ago the error in the transmitted ephemeris was 20 m, while the measurement error on a 10 km basis would have been 1 cm.

Why use accurate ephemeris?

First, it is necessary to keep in mind that the error values given earlier are valid for lines that have fixed solutions. However, on lines of the order of 50 km and above, it is very difficult to obtain a fixed solution using the transmitted ephemeris. Using accurate ephemeris greatly increases the chances of getting a fixed solution.

Secondly, it has long been known that height is determined less accurately using GPS than plan coordinates. Therefore, for work that requires better height determination, it is recommended to use accurate ephemeris.

Thirdly, we must remember that the transmitted ephemeris is only assumption about where the satellites should be. Sometimes situations may arise when the transmitted ephemeris contains errors that cannot but affect the quality of the baseline solution. A way out of this situation can be the use of fast ephemeris, a day after the observations are made.

Where can I find accurate ephemeris?

There are many sources where you can find different types of ephemeris for free. As examples, we can cite the website of the International Geodynamic Survey (IGS):
http://igscb.jpl.nasa.gov/components/prods.html

What is the most common format for accurate ephemeris?

Accurate ephemeris is available in two standard formats: SP3(ASCII format) and E18(binary format). Most professional GPS measurement processing programs directly support one of these two formats (for example, it supports both types of precise ephemeris, translator's note). If necessary, you can use a utility to translate between these two formats.

The processes occurring in modern technology are a mystery to the user. Moreover, often the user doesn’t care about them at all: either he’s not interested, or he just doesn’t care. This also applies to navigators. Turn it on - and you know your coordinates. A few finger movements and the route is ready. However, sometimes, in order to understand the technical characteristics of the same navigator, you need to know more than is necessary just to use it.

Therefore, I’ll make a reservation right away: the article will be of interest to those who are not satisfied with the role of an ordinary user of a “black box with a screen.” For those who seek to study all points of the technical characteristics of the device before purchasing it. For those who enjoy understanding the processes occurring in a variety of devices.

Such people do not answer “I don’t know” to questions like: “What processor is installed on your computer?” The question is, in fact, elementary, but you will be surprised at what percentage of your friends and comrades know the answer to it. Try it!

A little about the terms

Every field of science and technology is full of terms. These terms sound mysterious to the uninitiated, but become generally clear upon closer examination.

There are also many terms in the theory of space navigation. And it is not surprising: this area of knowledge is connected with the movement of satellites in near-Earth space, and with the reception, processing and transmission of signals, and with their coding.

Terms that may be useful to consider are the concepts of almanac and ephemeris. Why are these particular concepts interesting to us? Yes, because the understanding of the “cold” and “hot” start of the navigator is based on knowledge of these concepts.

Almanac in modern navigation and more

Even before the era of space navigation began, the concept of an almanac already existed. An almanac was a reference book that contains basic astronomical data - the positions of celestial bodies and their connection to the calendar. One of the oldest almanacs is the Chinese book Tong Xing.

Today, the purpose of almanacs has not changed. What has changed is the amount of data they contain and its accuracy. Almanac in space navigation is a collection of data on the main parameters of satellite orbits in the navigation system. The form in which this data is presented is, in fact, not so important for us.

The almanac contains six parameters of the satellite's orbit at a certain point in time. Moreover, each satellite of the system has data about other satellites. The navigator, having established communication with just one satellite, after receiving the almanac, has data on orbital parameters and others. An almanac loaded into the satellite's memory is valid for 30 days. Nevertheless, these data are updated more often - once every few days, during a communication session with one of the ground stations.

Ephemerides

In addition to the basic orbital parameters, the navigator receives their ephemerides from each of the satellites; this is data from which orbital deviations, disturbance coefficients, etc. are calculated. That is, with their help, the navigator can determine the location of satellites with high accuracy.

Ephemerides, which contain more accurate data, become outdated much sooner. Their data is only active for about 30 minutes. They are also updated by ground stations.

Without data on the location of navigation satellites, it is impossible to determine the coordinates of the receiver. This requires as many as four satellites. We will talk about the features of turning on the navigator and about “cold”, “warm” and “hot” starts in the next article.

What is a “cold” and “hot” start of a navigator?

General algorithm of the navigator

It’s the general one – only the developers know everything down to the smallest detail. So, after turning on, the navigator begins to attempt to establish communication with one of the navigation satellites.

The first satellite with which communication has been established transmits an almanac to the navigator, which contains information about the basic parameters of the orbits of each satellite in the orbital constellation of this particular navigation system.

One satellite is not enough to determine coordinates. For this, for example, a GPS navigation system requires at least four of them. Each of these four transmits its ephemeris to the navigator - a set of updated data about its orbit.

In general, nothing complicated, but just like that, we quietly got to the stage at which the difference between these two types of navigator start will be revealed.

Cold start

When you turn on the navigator for the first time or after a long break in its use, you will have to wait until you receive your own coordinates. How many? Depends on many factors:
- on the quality of the navigator receiving unit;
- on the number of satellites in the radio visibility zone;
- on the state of the atmosphere;
- on the level of electromagnetic noise at fundamental frequencies.

During the so-called “cold” start of the navigator, both the almanac and the ephemeris are completely absent from its memory. Or maybe they are present, but they are hopelessly outdated.

In this case, the navigator must go through the full cycle of obtaining this data.

The algorithm of his actions is approximately as follows:
- establish contact with the first of the found satellites;
- get the almanac, save;
- receive ephemeris from the found satellite, save;
- establish contact with three more satellites, receive ephemeris from them, save;

Lots of action, right? All this takes time. That’s why the start is called “cold” - the navigator needs time to “warm up” and prepare for work.

"Hot" start

It is radically different from the “cold” one in that at the time of switching on, the navigator’s memory already contains the current almanac and current ephemeris. We remember that the almanac data is valid for 30 days, and the ephemeris data is valid for 30 minutes.

This means that the start can be “hot” only when the power is turned off only for a very short time.

The navigator operation algorithm will be significantly simplified:
- establish communication with satellites;
- if necessary, update the ephemeris and save;
- based on the ephemeris, knowing the location of the satellites, calculate your own coordinates.

"Warm" start

Briefly. The navigator has an up-to-date almanac, but all ephemeris without exception are outdated, which means that you only need to get them.

Let's put everything in its place

If you arrange in ascending order the time required for the navigator to determine the receiver after turning it on, you get the following sequence: “hot”, “warm”, “cold” starts.

Now the navigator characteristic “cold/hot start time” will not only not confuse a knowledgeable person, but will also provide an opportunity to demonstrate their knowledge. But it’s not all that difficult!

In the algorithm for the operation of the navigator during “cold” and “hot” starts, mention was made of the navigator calculating its coordinates.

How does the navigator determine its coordinates?

It has been mentioned more than once that in order for a navigator to determine its coordinates, four satellites are needed. Why exactly four and what is the general scheme of this process, let’s try to figure it out right now.

In simple words about the complex

Electromagnetic radiation moves in space at a finite speed - the speed of light. Based on this, it is possible, by measuring the interval between the moment the signal begins to be transmitted and the moment it is received, to determine the distance between the transmitter and the receiver.

The navigator, having established communication with the satellites, having the almanac and ephemeris loaded into memory, receives a signal with an exact time stamp from each of the satellites. Using its internal clock, the navigator determines the time it took for the signal to reach it. Knowing the speed of signal propagation and time, the navigator solves a simple problem - calculates the distance at which it is from the satellite.

We turn on three-dimensional thinking. To unambiguously determine a position in three-dimensional space relative to points with known coordinates, it is necessary to know where at least three points are located.

Knowing the exact coordinates of three satellites at a certain point in time (thanks to the almanac and ephemeris) and the distances to them, the navigator determines its coordinates on the surface of the globe. Already in relation to two-dimensional coordinates accepted in cartography (longitude and latitude), and to altitude above sea level.

Three were dealt with. Now let's deal with the fourth satellite.

Don't think down on seconds

And if we are talking about space navigation and the speed of light, then you cannot think down even about microseconds. The slightest error in measuring the time it takes a signal to travel the distance from the navigator to the satellite can result in hundreds of meters, or even kilometers.

Time measurement accuracy is the weak point of any navigation system.

Each of the satellites is equipped with very accurate (and expensive and large) atomic clocks, the accuracy of which is nanoseconds (this is 10 -9). Navigators are equipped with a much less accurate clock - based on a quartz oscillator.

It is for time synchronization in the navigator system that there are three satellites and a fourth is needed. It synchronizes time and minimizes errors that arise from inaccurate time measurements. Or rather, it forces the satellite and the navigator to generate the same code at the same time. This code is transmitted in the very signal by which the distance is measured. Having received a signal with a code, the navigator determines how long ago it itself generated such a code.

This is the scheme in general terms. In reality, everything is much more complicated: the digital signal is encoded, time synchronization, calculating the coordinates of satellites and one’s location are not at all simple tasks. Everything is further complicated by the fact that developers use various tricks to improve the accuracy of measurements: noise-resistant coding, corrections to level out the influence of the Doppler effect, corrections for changes in the speed of radio signal transmission in the troposphere and ionosphere.

But this is not the topic of a short explanatory article, but of a much more serious and voluminous work.

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GPS Basics: Using High-Precision Ephemeris in Measurement Processing.

What are ephemeris?

In the famous Webster's Dictionary of Definitions, the following definition of the term ephemeris is given: “An ephemeris is a table of coordinates of a celestial body given at various periods of time for a certain period. Astronomers and surveyors use ephemeris to determine the positions of celestial bodies, which are later taken to calculate the coordinates of points on the earth's surface.

Transmitted (on-board) ephemeris

Accurate ephemeris (Final products)

Accurate ephemeris consists of the Earth-wide geocentric coordinates of each satellite as defined in the Earth-wide Reporting System and includes clock corrections. Ephemeris are calculated for each satellite at 15 min intervals. Accurate ephemeris is a post-processing product. Data is collected by tracking stations located throughout the Earth. This data is then transmitted to the International GPS Service (IGS), where the exact ephemeris is calculated. Accurate ephemeris becomes available approximately 2 weeks after the time of data collection and has an accuracy of less than 5 cm and 0.1 ns.

The exact ephemeris can be downloaded from the NASA server:
ftp://igscb.jpl.nasa.gov/igscb/product/

Rapid ephemeris (Rapid products)

Fast ephemeris can be downloaded from the IGS server:

Predicted or Ultrafast ephemeris (Ultrarapid products)

Ultrafast ephemeris can be downloaded from the IGS server:
http://igscb.jpl.nasa.gov/ components/dcnav/igscb_ product_wwww.html

Do we need accurate ephemeris?

Why use accurate ephemeris?

Thirdly, we must remember that the transmitted ephemeris is only an assumption of where the satellites should be. Sometimes situations may arise when the transmitted ephemeris contains errors that cannot but affect the quality of the baseline solution. A way out of this situation can be the use of fast ephemeris, a day after the observations are made.

Where can I find accurate ephemeris?

What is the most common format for accurate ephemeris?

Accurate ephemeris is available in two standard formats: SP3 (ASCII format) and E18 (binary format). Most professional GPS measurement processing programs directly support one of these two formats (for example, Trimble Geomatics Office supports both types of precise ephemeris, translator's note). If necessary, you can use a utility to translate between these two formats.

How are the names of precise ephemeris files formed?

If this is your first time using precision ephemeris, the file names may seem complicated and lack logical structure. However, in reality, everything turns out to be not so complicated. The exact ephemeris file names are zzznnnnx.aaa, where

zzz – name of the organization (NGS, IGS, etc.)
nnnn – GPS week serial number (for example 0475)
x – day of the week (Sunday=0, Saturday=6)
aaa – file type (for example, sp3, e18)

GLOBAL POSITIONING SYSTEMS

1. MEASUREMENT MODES, MEASURED VARIABLES

Code mode is the mode originally built into the system. The signal of each satellite contains its ephemeris - data about the location of the satellite, which allows you to calculate the coordinates of the satellite in the earth's coordinate system. In addition, the code signal contains a timestamp transmitted every six seconds. The moment the time stamp leaves the satellite, determined by the satellite's clock, is signed on it. The receiver captures the satellite signal, identifies the satellite by its signal code, reads the timestamp and determines the time t r the signal travels from the satellite to the receiver. This allows you to calculate the range from the receiver to the satellite. Everything would be exactly like this if the clocks of the receiver and the satellite were synchronous. In fact, there is a non-zero difference between their readings at the same moment in time - the relative correction of the clock. It is included in the range determination result. Therefore, in this case, the range is called pseudo range. They say that in the code navigation mode the measured value is the code pseudorange. The correction of the receiver clock relative to the satellite clock at the time of observations is determined as an unknown quantity from processing the results of these observations.

Thus, for each point there are not three unknowns - three coordinates of the point - but four unknowns: three coordinates and the receiver clock correction. Therefore, to instantly determine the location, it is necessary that signals from at least four satellites of the system simultaneously arrive at the receiver antenna. The system's constellation of satellites provides this requirement.

Phase mode is a mode of high-precision geodetic measurements. It involves at least two receivers simultaneously. In this mode, the coordinates of the base vector are obtained, that is, the difference in the coordinates of the points at which the satellite receiver antennas are installed. The error in determining the base vector ranges from several millimeters to several centimeters. The measurements are performed at the carrier frequency of the satellite signal, freed from the code by the squaring procedure. The measured quantity is the instantaneous phase difference between the satellite signal and the receiver generator signal. Here it is appropriate to talk about the terms absolute and relative definitions. According to more or less established terminology, absolute definitions mean determining the coordinates of a point, that is, working in code navigation mode. Relative definitions mean determining the location of one point relative to another - a solid, starting point. This is the difference phase regime of geodetic measurements. Relative definitions can also be called differential navigation code mode, when the location and speed vector of the mobile carrier are determined relative to the differential station.

The Doppler mode, more precisely the integral Doppler mode, is, as it were, secondary to the phase one. The Doppler frequency is proportional to the rate of phase change, so the Doppler frequency is obtained simultaneously with the phase measurement, without any additional costs. Despite the “free” mode, this mode provides rich information about the location of the point. It should be recalled that the first satellite radio navigation systems were exclusively Doppler.

As stated, observing modes are inextricably linked to each other. The surveyor is most interested in the high-precision phase regime, but he obtains the approximate coordinates of points necessary for adjustment from code and Doppler measurements. Navigating around an object and finding starting points also makes it very easy to use the code navigation mode. Next, let's look at the measured values in more detail.

1.1. Code pseudoranges

Each satellite in the system emits carrier oscillations with a wavelength of about 20 centimeters, manipulated in phase by code sequences. The structure of the signal is described in more detail in Section 3. Here we will say that all GPS satellites operate on the same carrier frequencies, but each satellite has its own individual code. The satellite receiver generates copies of each satellite's code and identifies the satellites precisely by the shape of the code. Immediately after turning on the receiver, it begins to capture satellite signals. In other words, the receiver performs correlation processing of the satellite signal and the copies of codes generated by this receiver, searching through these copies. If the correlation function differs from zero, it means that the satellite is identified and its signal is captured.

After capturing the signal from the first satellite, the receiver begins to download the code information contained in the navigation satellite message. In particular, the almanac is downloaded. This is discussed in more detail in section 3.2. Sometimes the receiver independently decides to switch to downloading information from another, more “convenient”, in its opinion, satellite, usually located closest to the zenith of the observation point. The entire procedure is reflected on the display, the operator can observe it, but cannot intervene. After acquiring signals from a sufficient number of satellites, the receiver begins to determine the navigation coordinates of its antenna from the measured pseudo-range codes. To determine all three antenna coordinates, it is necessary to work with four satellites. This mode is designated 3D (3 Dimensional) - three-dimensional. Navigation receivers provide the ability to work in two-dimensional 2D mode. The receiver, while it managed to capture the signal of only three satellites, determines the planned coordinates of the point. After acquiring the signal from the fourth satellite, the receiver switches to 3D mode.

Code pseudoranges are determined from correlation processing of the satellite code signal and a copy of this signal generated by the receiver. The satellite's C/A-code and P-code signals are accompanied by time stamps generated by the satellite frequency and time standard - the satellite clock. Similarly, the receiver code signals are accompanied by timestamps generated by the receiver clock. During correlation processing, a search is made for the maximum correlation coefficient of two signals. As a result, the relative time delay of the two signals is obtained as the time interval between time stamps of the same name. This time interval, corrected for signal delays in the atmosphere and for the influence of a number of factors and multiplied by the speed of the signal, gives the pseudorange. It is calculated using the formula for the case of a single passage of a signal over a distance. The difference is that the result is distorted by the correction of the receiver clock relative to the satellite clock. In physical essence, the measurement of code pseudo-ranges is performed by implementing a time-based measurement method with code modulation of a signal passing the distance once. Knowing the coordinates of the satellites at the time of observations from the navigation message and using the measured pseudo-range values, the receiver determines the coordinates of the antenna. The task is similar to linear spatial intersection. The difference is that in addition to the antenna coordinates, the receiver clock correction is received. The measurement error is characterized by URA (User Range Accuracy) - the accuracy of range measurements (to each satellite) for a given user. The error in determining coordinates and clock correction also depends on the geometry of the observations. All this information is also displayed on the display. The geometric factor is described in section 1.4.

Brief description