1 Overview of GNSS
According to the principle of resection positioning, in order to achieve GNSS positioning, two problems need to be solved: one is to observe the spatial position of the satellite at an instant; the other is the distance between the observation site and the satellite, that is, the coordinates of the satellite in a certain coordinate system.
To this end, it is first necessary to establish an appropriate coordinate system to characterize the reference position of the satellite [8], and the coordinates are often related to time [9]. Therefore, GNSS positioning is based on the coordinate system and the time system.
2 Coordinate system and time system
In the satellite navigation system, the coordinate system is used to describe and study the motion of the satellite in its orbit, express the position of the ground observation station and process the positioning observation data. Depending on the application, the selected coordinate system is also different.
Coordinate systems are roughly divided into the following categories: geographic coordinate system, inertial coordinate system, earth coordinate system, geocentric coordinate system and ginseng coordinate system.
Coordinate systems commonly used in China are: 1954 Beijing 54 Coordinate System (Beijing 54 Coordinate System, P54), 1980 National Geodetic Coordinate System (National Geodetic Coordinate System 1980, C80), 1984 World Geodetic Coordinate System (World Geodetic System-1984 Coordinate System, WGS-84), 2000 National Geodetic Coordinate System (China Geodetic Coord inateSystem2000, CGCS2000).
The time system is one of the most important and basic physical quantities in satellite navigation.
First, high-precision atomic clocks control all signals sent by satellites.
Second, in most satellite navigation systems, distance is measured by precisely timing the signal's propagation time.
The time system mainly includes universal time, ephemeris time, mechanical time, atomic time, coordinated universal time, Julian day, satellite navigation time system.
Among them, GNSS adopts an independent time system as the basis for navigation and positioning calculation, which is called GNSS time system, or GNSST for short. GNSST belongs to the atomic time system, and its second is the same as the atomic time second.
3 Positioning principle
The design idea of GNSS is to use artificial satellites in space as reference points to determine the spatial position of an object. According to geometric theory, it can be proved that by accurately measuring the distance between a certain point on the earth and three artificial satellites, the position of this point can be determined in a triangle. This is the most basic design idea and positioning function of GNSS.
Assuming that the distance from a certain point P to satellite S1 measured on the ground is r1, then it can be seen from geometry that the possible space where point P is located can be concentrated on such a sphere, the center of which is satellite S1, and the radius is r1. Assume that the measured distance from point P to the second satellite S2 is r2, which also means that point P is located on a spherical surface with the second satellite S2 as the center and radius r2.
If the distance from point P to the third satellite S3 is measured as r3, it means that point P is also located on a spherical surface with the third satellite S3 as the center and radius r3, so that the position of point P can be determined, which is the intersection of the three spherical surfaces, as shown in Figure 3-2. From the basic principle of GNSS positioning, it can be seen that the essence of GNSS positioning method is the spatial resection of surveying. Because GNSS uses one-way ranging, and it is difficult to ensure strict synchronization between the satellite clock and the user receiver clock, the distance between the observation station and the satellite is affected by the asynchrony of the two clocks. The satellite clock error can be corrected by the relevant clock error parameters given in the navigation message, but the clock error of the receiver is mostly difficult to accurately determine. The usual optimization method is to use it as an unknown parameter and solve it together with the coordinates of the observation station, that is, it is generally necessary to solve 4 unknown parameters (3 point coordinate components and a clock error parameter) at an observation station. Therefore, at least 4 synchronous pseudo-range observations are required, that is, 4 satellites need to be observed simultaneously.
According to the motion state of the user station, GNSS can be divided into static positioning and dynamic positioning. Static positioning is to fix the point to be fixed, and place the receiver on the point to be fixed for a large number of repeated observations. Dynamic positioning means that the point to be fixed is in a moving state, and the point coordinates of the point to be fixed in motion at each observation time are measured, as well as the state parameters of the moving carrier, such as speed, time and orientation. In addition, it can also be divided into absolute positioning and relative positioning according to the positioning mode. Absolute positioning uses only one receiver for positioning, also known as single-point positioning, which determines the absolute position of the receiver antenna in the coordinate system. Relative positioning means that two receivers are placed on two fixed points to be fixed, or one point is fixed on a known point, and the other point is used as a floating point to be fixed. After a period of synchronous observation, the relative position between the two points can be determined to obtain high-precision position coordinates.
4 GNSS data error
The errors of the satellite navigation system can be divided into four categories from the sources: errors related to signal propagation, errors related to satellites, errors related to receivers, and errors related to the rotation of the earth [11].
Errors related to signal propagation include ionospheric delay error, tropospheric delay error and multipath error. Errors related to satellites include satellite ephemeris errors, satellite clock errors, and relativistic effects. Errors related to the receiver include receiver clock error, position error (receiver antenna phase center relative to station identification center) and antenna phase center position deviation. Errors related to the rotation of the Earth include effects from the Earth's tides and the Earth's rotation.
The error classification is shown in Table 3-1. Several common errors are listed below for illustration.
4.1 Ionospheric delay error
The ionosphere is the atmospheric layer at an altitude of 50-1000 km above the earth. Neutral molecules in this atmosphere are ionized by solar radiation, producing a large number of positive ions and electrons. In the ionosphere, the transmission rate of electromagnetic waves is related to the electron density. Therefore, the distance obtained by directly multiplying the propagation speed of electromagnetic waves in vacuum by the propagation time of the signal may not be equal to the real geometric distance between the satellite and the receiver. The deviation between the two distances is called the ionospheric delay error.
Ionospheric delay error is one of the main error sources affecting satellite positioning. It causes a relatively large distance error, generally up to 15m during the day and 3m at night; and the maximum error caused by the zenith direction can reach 50m, and the maximum error caused by the horizontal direction can reach 150m.
Improving measures for ionospheric delay errors usually include using dual-frequency observations, using ionospheric models supplemented by corrections, and using synchronous observations to calculate the difference.
4.2 Multipath error
When the receiver receives the signal, if the signal reflected by the objects around the receiver also enters the antenna, and propagates through different paths with the signal from the satellite and arrives at the receiving end at different times, the reflected signal and the direct signal from the satellite will superimpose and interfere with each other, distorting or generating errors in the original signal, resulting in fading [12]. This fading caused by multipath signal propagation is called multipath effect, also known as multipath effect.
Multipath error is a major source of error in satellite navigation systems, which can damage the accuracy of satellite positioning, and even cause loss of signal lock in severe cases. The improvement measures usually include placing the receiver antenna away from the strong transmitting surface, selecting an anti-multipath antenna, appropriately extending the observation time, reducing the periodic impact, improving the circuit design of the receiver, improving anti-multipath signal processing and adaptive cancellation technology.
4.3 Satellite ephemeris error
The difference between the satellite position given by the ephemeris and the actual position of the satellite is called the satellite ephemeris error. Satellite ephemeris errors are mainly produced by clock error, frequency offset, and frequency drift. In view of the comprehensive influence of various perturbation forces on satellites during motion, it is difficult for ground monitoring stations to measure these forces accurately and reliably and to grasp the laws of their action for the current technology. Therefore, the estimation and processing of satellite ephemeris errors is particularly critical.
The improvement measures usually include ignoring the orbit error, processing the observation data through the orbit improvement method, using precise ephemeris and calculating the difference of the synchronous observation value.
5 Differential GNSS positioning technology
Reducing or even eliminating the errors mentioned in Section 3.1.3 is one of the measures to improve positioning accuracy, and differential GNSS can effectively use the reference stations with known positions to estimate the common errors, and weaken or eliminate some errors through related compensation algorithms, thereby improving positioning accuracy.
The basic principle of differential GNSS is to set up one or more receivers within a certain geographical range, and use a receiver with known precise coordinates as a differential reference station. The reference station continuously receives GNSS signals and compares them with the known position and distance data of the reference station to calculate the differential correction amount. Then, the base station will send this differential correction to the rover within its range for data correction, thereby reducing or even eliminating errors caused by satellite clocks, satellite ephemeris, ionospheric delay and tropospheric delay, and improving positioning accuracy.
The distance between the rover and the differential reference station directly affects the effect of differential GNSS. The closer the distance between the rover and the differential reference station, the stronger the correlation of measurement errors between the two stations, and the better the performance of the differential GNSS system.
According to the different target parameters of differential correction, differential GNSS is mainly divided into position difference, pseudorange difference and carrier phase difference. The following will briefly introduce position difference, pseudorange difference and carrier phase difference.
5.1 Position difference
The position differential system is shown in Figure 3-3.
By installing a GNSS receiver on a reference station with known coordinate points to observe 4 or more satellites in real time, the positioning can be performed and the coordinate measurement value of the current reference station can be obtained. In fact, due to the existence of errors, the coordinates obtained by solving (Solve) the message received by the GNSS receiver are different from the known coordinates of the reference station.
Then take the difference between the measured coordinate value and the actual coordinate value of the reference station as the differential correction amount. The reference station uses the data link to send the obtained differential correction to the rover, and the rover uses the received differential correction and the measured value received by its own GNSS receiver to modify the coordinates. Position difference is the simplest difference method, which transmits a small number of difference corrections and is simple to calculate, and any GNSS receiver can be refitted and composed of this difference system.
However, since the rover and the reference station must observe the same set of satellites, the application range of the position difference method is limited by the distance. Usually, the distance between the rover and the reference station does not exceed 100km.
5.2 Pseudorange difference
As shown in Figure 3-4, the pseudo-range differential technology is to set one or more known points installed with GNSS receivers as a reference station within a certain range of positioning area, and continuously track and observe the pseudo-ranges of all GNSS satellites within the signal receiving range. The real geometric distance from the satellite to the reference station is obtained by using the known coordinates on the reference station, and compared with the observed pseudo-range, and then the difference is filtered by a filter to obtain its pseudo-range correction value.
Next, the base station sends all pseudorange correction values to the rover, and the rover uses these error values to correct the pseudoranges measured by GNSS satellite transmissions.
Finally, the user uses the corrected pseudorange for positioning.
There is a strong correlation between the measurement error and the distance between the reference station and the rover station of pseudo-range difference, so within a certain area, the smaller the distance between the rover station and the reference station, the higher the positioning accuracy obtained by using GNSS difference.
5.3 Carrier phase difference
GNSS position difference technology and pseudo-range difference technology can basically meet the positioning accuracy requirements of positioning and navigation [13], but it is far from enough to be applied in automatic driving. Therefore, more accurate GNSS difference technology, namely carrier phase difference technology is needed.
There are correction method and difference method for carrier phase difference.
The correction method is similar to the pseudo-range difference. The base station sends the carrier phase correction amount to the rover to correct its carrier phase observation value, and then obtain its own coordinates.
The difference method is to send the carrier phase measurement value observed by the base station to the rover, so that it can calculate the difference correction amount by itself, so as to realize the difference positioning.
The basis of carrier difference technology is to process the carrier phase of two measuring stations in real time. Compared with other differential techniques, in the carrier phase differential technique, the reference station does not directly transmit the differential corrections related to the GNSS measurement, but sends the original value of the GNSS measurement. After the rover receives the data from the reference station, it forms a phase difference observation value with the data of its own observation satellite, uses the combined measurement value to obtain the baseline vector to complete the relative positioning, and then calculates the coordinates of the measurement point.
However, when using the carrier difference method for phase measurement, each phase observation contains an unknown integer number of cycles that cannot be directly observed by the carrier, which is called phase integer ambiguity. How to correctly determine the phase integer ambiguity is the most important and also the most difficult problem in the solution of carrier phase measurement. Solving the phase integer ambiguity can be divided into methods with initialization and methods without initialization. The former requires an initialization process, that is, to conduct fixed observations on the rover for a certain period of time, which generally takes 15 minutes. The static relative measurement software is used to solve the problem to obtain the phase integer ambiguity of each satellite and fix this value, which is convenient for solving the phase integer ambiguity as a known quantity in the future dynamic measurement. Although the latter is called no initialization, it actually still needs a short initialization process, usually only 3~5min, and then quickly solves the phase integer ambiguity.
Therefore, the two methods for solving the phase ambiguity need to have an initialization process, and the satellite signal must not be lost after initialization, otherwise, it is necessary to return to the starting point to capture and lock again.
RTK is a technology that uses receivers to observe the carrier phase of satellite signals in real time. It combines data communication technology and satellite positioning technology, and adopts real-time calculation and data processing methods to provide real-time three-dimensional coordinate points in the designated coordinate system for the rover, and achieve high-precision position positioning in a very short time. Commonly used RTK positioning technologies are divided into conventional RTK and network RTK.
5.3.1 Conventional RTK
Conventional RTK positioning technology is a real-time dynamic differential positioning technology based on GNSS high-precision carrier phase observations, and can also be used for fast static positioning.
When conventional RTK is used for positioning work, in addition to the base station receiver and rover receiver, data communication equipment is also required. The base station broadcasts the carrier phase observation value and station coordinates obtained by itself to the dynamic users working around it in real time through the data link.
The rover data processing module determines the position of the rover relative to the reference station through dynamic differential positioning, and obtains its own instantaneous absolute position according to the coordinates of the reference station. The conventional RTK system is shown in Figure 3-5.
Obviously, conventional RTK positioning technology can meet the requirements of many applications, but the distance between the rover and the reference station should not be too far. When the distance is greater than 50km, conventional RTK can only achieve decimeter-level positioning accuracy.
Therefore, conventional RTK cannot fully meet the centimeter-level positioning requirements of the automatic driving system for cars, lanes and obstacles.
5.3.1 Network RTK
5.3.1.1 Principle of network RTK
Network RTK is also called multi-base station RTK.
Network RTK belongs to real-time carrier phase double-difference positioning, which is a new real-time dynamic positioning technology developed based on conventional RTK and differential GNSS technology in recent years.
Network RTK refers to a network of reference stations formed by several fixed and continuously operating GNSS reference stations in a certain area, covering the area in all directions, and using one or more of these reference stations as a reference to provide GNSS error correction information for GNSS users in the area to achieve real-time and high-precision positioning.
Compared with conventional RTK technology, network RTK technology has wider coverage, lower operation cost, higher positioning accuracy and shorter initialization time for user positioning.
5.3.1.2 Network RTK system
The network RTK system is shown in Figure 3-6. It is an application example of network RTK technology, mainly including fixed base station network, control center part responsible for data processing, data broadcast center, data link and user station.
The base station network consists of several base stations, each of which is equipped with dual-frequency full-wavelength GNSS receivers, data communication equipment and meteorological instruments.
The coordinates of the reference station can be obtained accurately through long-term GNSS static relative positioning and other methods. The GNSS receiver of the reference station performs continuous observation at a certain sampling rate, and transmits the observation data to the data processing center in real time through the data link. The data processing center first performs preprocessing and quality analysis on the data of each station, and then performs unified calculation on the data of the entire reference station network, estimates the correction items of various system errors (ionosphere, troposphere and orbit errors) in the network in real time, and establishes an error model.
According to different communication methods, the network RTK system can be divided into one-way data communication and two-way data communication.
In one-way data communication, the data processing center broadcasts the error parameters directly through the data broadcasting device. After receiving these error correction parameters, the user calculates the error correction number according to his own coordinates and the corresponding error correction model, so as to perform high-precision positioning. In the two-way data communication, the data processing center listens in real time to the service request of the rover, and receives the approximate coordinates from the rover, and calculates the error at the rover according to the approximate coordinates and error model of the rover, and then directly broadcasts the correction number or virtual observation value to the user. The data communication between the reference station and the data processing center can be carried out by wireless communication and other methods. The two-way data communication between the rover and the data processing center can be realized through vehicle networking communication technologies such as V2X.