GEOM 3010 - Fundamentals of GNSS 2024 PDF

GEOM 3010 ‐ Field Surveying 3 Fundamentals of Global Navigation Satellite Systems Global Navigation Satellite Systems Satellite positioning systems began in United State of America in 1958 with the Navy Navigation Satellite System (NNSS), more commonly referred to as the TRANSIT system. The system...

GEOM 3010 ‐ Field Surveying 3 Fundamentals of Global Navigation Satellite Systems Global Navigation Satellite Systems Satellite positioning systems began in United State of America in 1958 with the Navy Navigation Satellite System (NNSS), more commonly referred to as the TRANSIT system. The system worked off the principle of the Doppler Effect. The Doppler effect is observed whenever the source of waves is moving with respect to an observer. The effect of a moving source of waves produces an apparent upward shift in frequency for observers while the source of the wave is approaching, and an apparent downward shift in frequency for observers as the wave source is receding. The observed changes in frequency are in signals transmitted by satellites are observed by receivers in ground stations. These observed doppler shifts are a function of the distance to the satellite and their direction of movement in relation to the ground station. The transmitting frequencies of the satellites are known, as well as the trajectory of the satellites. Together with precise timing, the position of the ground station can be determined. Public access to the TRANSIT system was granted in 1967. NNSS went through several iterations before being decommissioned by the U.S. December 31, 1980. Foreign systems remained active until the early 1990s. The satellite navigation project was expanded in the 1970s with the development of the NAVigation Satellite Timing And Ranging Global Positioning System (NAVSTAR GPS, or GPS for short) by the U.S. Department of the Navy, with the first satellites being launched in 1978. Since then several other Global Positioning Systems have been developed and launched; The former Soviet Union’s GLONASS system, Japan’s QzSS system, European Space Organization’s Galileo System, and China National Space Administration’s BeiDou system, just to name a few. The scope of all these satellite positioning systems is now referred to as Global Navigational Satellite Systems (GNSS). Modern receivers generally capable of receiving signals from a combination of systems and are referred as such as GNSS receivers, while those that ONLY receive GPS signals are referred to as GPS receivers. Overview of Satellite Positioning Systems Satellite positioning systems use signal information and precise timing to compute accurate positions of receivers. In these types of systems, the satellites are the reference (or control) stations, the distances (or ranges) from the satellites to the receiver are calculated, and those ranges are used to calculate the position of the receiver through Multilateration. Trilateration or Multilateration is the use of ranges (3 for Trilateration, 4 or more for Multilateration) for determining coordinates of an unknown position. This process can be compared to resection in conventional surveying methods, where a combination of angles and distances to reference stations are used to determine an unknown position of an instrument. 1|Page Satellite positioning systems are combination of three segments: the Space segment (satellites), the Control segment (monitoring stations), and the User segment (receivers). 1: GPS System Components The Space segment would refer to the satellites of a specific constellation. For GPS this refers to 32 satellites (24 operational, 8 in reserve) in medium earth orbit (~20,200 km) currently operating in six orbital planes spaced at 60° intervals around the equator. Other systems operate in slightly different orbital planes and have varying number of satellites depending on their development at the time. These configurations provide constant 24 hour of coverage. Each satellite has a 12- hour orbital period, passing over the same location twice per day. Individual satellites are identified using a unique Psuedo Random Noise (PRN) number, also known as a Satellite Vehicle Number (SVN). Atomic clocks are used on the satellites to provide precise and accurate timing information which is encoded into the signals transmitted by the satellites. The Control segment consists of monitoring stations which track the signals and the position of the satellites over time. Monitoring stations are located at several locations around the world for each of the GNSS constellations. Each of these monitoring stations then relates the information to a master control station. Monitoring data is then used to make precise, near- future predictions of the orbits of each of the satellites, and their clock correction biases. These orbital predictions and biases are then broadcast as part of the satellite signal which the receivers use to determine the ranges to the individual satellites being observed. 2|Page The User segment is comprised of the military (Precise Positioning Service (PPS)) and civilian (Standard Positioning Service (SPS)) users. The Precise Positioning Service (PPS) is a highly accurate military positioning, velocity and timing service is available on a continuous, worldwide basis to users authorized by the U.S. Government. P(Y) code capable military user equipment provides a predictable positioning accuracy of 2.7 meters horizontally and 4.9 meters vertically and time transfer accuracy to UTC within 40 nanoseconds or better (at a 95% confidence interval). PPS is highly encrypted data transmitted on both the GPS L1 and L2 frequencies and is designed primarily for U.S. military use. Only those with sufficient U.S. Military clearance are authorized to use PPS and the encryption tools needed to use the service. 2: Satellite availability The Standard Positioning Service (SPS) is a positioning and timing service which is available to all GPS users on a continuous, worldwide basis with no direct charge. SPS is provided on the GPS L1 frequency which contains a coarse acquisition (C/A) code and a navigation data message. SPS provides a predictable positioning accuracy of 9 meters horizontally and 15 meters vertically, and time transfer accuracy to UTC within 40 nanoseconds (at a 95% confidence). GNSS Signals Satellite ranges are measured with signals broadcast within the microwave portion of the electro- magnetic spectrum from satellites to receivers. The system is passive, in that the satellites broadcast and the receivers only receive those broadcasts. Because of this, any number of receivers can be receiving at any time. The broadcast signal contains a massive amount of information which the receiver uses to determine a geographic position. This information is encoded on carrier waves broadcast from a radio on each of the satellites. Each carrier phase broadcast maybe encoded with several codes. 3|Page Time Range from the satellite to the receiver is determined by the amount of time lapsed between the time the signal was broadcast to when it was received. The range is a function of time, and the precision of that measurement is crucial to the determination of the range measurement. 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑅𝑎𝑡𝑒 𝑇𝑖𝑚𝑒 𝐶 𝑇𝑖𝑚𝑒 𝑇𝑖𝑚𝑒 𝐶 ∆𝑡 Time keeping on the satellites is regulated using highly precise atomic clocks. Time keeping on the receivers are done with quartz crystal clocks, the quality of which is generally regulated by the quality of the receiver. GPS time is expressed with a resolution of 1.5 seconds as a week number and a time of week count (TOW). The zero point (week 0, TOW 0) is defined as 1980-01-06T00:00Z. The TOW count is a value ranging from 0 to 403,199 whose meaning is the number of 1.5 second periods elapsed since the beginning of the GPS week. To express TOW count requires 19 bits (219 = 524,288) of data. GPS time is a continuous time scale in that it does not include leap seconds. So, the start and end of GPS weeks may differ from that of the corresponding UTC Day by an integer number of seconds. GPS Signals Historically, GPS satellites use two carrier phase frequencies to broadcast signals known as L1 and L2. L1 has a frequency of 1575.42 MHz, L2 has a frequency of 1227.60 MHz. L1 signals were modulated with the precise P(Y) code, as well as the civilian coarse acquisition code (C/A code). The C/A code allows receivers to acquire satellites and determine their approximated positions. L2 was modulated with the broadcast message and the P(Y) code. Modern positioning satellites use additional signals and updated codes. Currently, GPS satellites use three carrier phase frequencies to broadcast signals: L1, L2, and L5 (1176.45 MHz). Two additional civilian acquisition codes have been added to L1 and L2 signals, L1C and L2C. Military P(Y) code is now replaced with M Codes across all three signal bands. GLONASS Signals GLONASS is a similar system to NAVSTAR GPS, in that both provide real time positioning, timing, and velocity information to both military and civilian users. GLONASS satellites are also at a middle earth orbit of ~19,100 km, with an inclination of 64.8°. GLONASS uses an L1 and L2 signal like GPS. However, they use frequency-division multiple access (FDMA) to differentiate between the satellites. Where each GPS satellite has its own PRN to identify which satellite is being received as part of the C/A code, GLONASS satellites each broadcast at a specific frequency in the L1 and band. Satellites are determined by their frequency on either side of the 1602.0 MHz L1 band, and 1246.0 MHz for the L2 band. 𝐿1𝑂𝐹 1602.01 𝑀𝐻𝑧 𝑛 0.5625 𝑀𝐻𝑧 𝐿2𝑂𝐹 1246.0 𝑀𝐻𝑧 𝑛 0.4375 𝑀𝐻𝑧 4|Page  𝑤ℎ𝑒𝑟𝑒: 𝑛 𝑠𝑎𝑡𝑒𝑙𝑙𝑖𝑡𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑛𝑢𝑚𝑏𝑒𝑟 6, … ,0, … 6 Since 2008 GLONASS has been using code-division multiple access (CDMA), like GPS, Galileo, and BeiDou. CDMA supplies a PRN to identify which satellite is being, as all satellites are broadcasting at the same frequencies. GLONASS has also added a third signal, L3OF, centered at 1202.025 MHz. Galileo Signals Galileo constellation also contains 30 in-orbit satellites, at an altitude of ~23,200 km, in three orbital planes inclined at 56°, with 120° separation between the orbital planes. Galileo satellites transmit three signals: E1 (1575.42 MHz), E5 (1191.795 MHz), and E6 (1278.75 MHz). E5 is broken into two separate signals, E5a (1176.45 MHz) and E5b (1207.14 MHz), each is modulated with the same codes. BeiDou-3 Signals BeiDou’s current system, BDS-3, is comprised of 30 satellites in medium Earth orbit, and uses three signal bands B1 (1575.42 MHz), B2 (1191.79 MHz), and B3 (1268.52 MHz). Each of the three signals is modulated with several codes for both military and civilian access. BeiDou’s B1, B2 and B3 signals are overlapping with Galileo’s E1, E5, and E6 respectively for convenience of receiver design. Codes Each carrier phase signal is modulated, or encoded, with one or more codes. Codes are binary strings of computer language which provide navigation and timing information to the receiver. GPS satellites use three basic codes to convey information: P code, C/A code, and Navigation Code. Precision Code, or P-Code, is strictly for military and authorized usage only. P-Code is available on all three L bands (L1, L2 & L5), and is open to the public. However, the P code is encrypted with a W-code which required authorized decryption keys to be used. Coarse acquisition code, or C/A code, is broadcast on the L1 signal. C/A code contains the PRN SVN of each satellite allowing the receiver to identify which satellite vehicle is being received, as well as the rough position of the satellite in the sky. A version of C/A code is also broadcast in the L2 signal as the L2C code. Prior to the addition of the L2C code, receivers had to use GPS L1 signal to access the C/A code and resolve a solution. Adding the L2C code allows for more flexibility. Navigation code is modulated to both the P and C/A code. The navigation code contains the GPS time, date, and satellite health status, Keplerian parameters, as well as an almanac predicting the position of the satellite at any specific time, orbital parameter to refine that position, atmospheric information, and clock correction information for precise timing of the signal. The ephemeris and almanac data are only valid for 4 hours at a time. These messages are updated from the control segment to the satellites several times daily. Modern positioning satellites use 5|Page the upgrade CNAV navigation message which provides higher precision and detailed navigation message. Selective Availability Selective Availability (SA) was the intentional degradation of the public GPS signals for reasons of national security. The availability of the GPS signals can be regulated by the U.S. Department of the Navy to be more or less accurate in selective geographic reasons. (They can turn it off if they don’t want you to have it). SA was implemented for all areas outside of U.S. territories to limit availability to only U.S. users. SA was discontinued in 2000 to make GPS available globally. However, it can be turned on for specific areas when needed (i.e. areas of American military activity). Modulated Carrier Waves The various GNSS signals: B1, B2, B3, E1, E5, E6, L1, L2, L5, …, are carrier waves generated by oscillators built into the various satellites. A carrier wave is a harmonic electromagnetic wave which is a pure continuous sinusoidal wave with a single constant frequency and amplitude. These waves are how wireless broadcast messages are generally sent. These carrier waves are modulated to carry information. By changing the amplitude of the carrier wave using an audio signal, such as voice or music, is amplitude modulation and is used for AM radio broadcast. Modulating the carrier by changing its instantaneous frequency is frequency modulation, or FM Radio. FM signals carry more information allowing for high-fidelity broadcasting. GNSS Signals work by varying the instantaneous phase of the carrier, or phase modulation. GNSS carrier waves are phase-modulated with pseudorandom noise (PRN) codes (C/A, P, L1C, L2C, etc.) and navigation messages. GNSS receivers use the PRN codes to produce a pseudorange (estimated distance) observable with a precision in the sub-meter range. 3: Amplitude, frequency, and phase modulation Electronic Distance Meters (EDM) work in a similar manner. A carrier wave is sent from the instrument and is reflected to a receiver n the same instrument. Because the signal is a single constant frequency, the distance is simply a product of the time the signal traveled. However, GNSS carrier wave signals are not reflected to the satellite, the pseudorange (ρ) to the satellite is calculated using the synchronization of clocks in both the satellite and the receiver. This dependence on synchronization introduces a source of error into the range determination. One microsecond of discrepancy can result in ~300 meters of error in the range measurement. 6|Page  4: Satellite pseudorange Determining Position In order to determine a position a receiver must measure enough simultaneous satellite pseudoranges (ρ) to triangulate a position [(X,Y,Z) 3D position] and the synchronization of the receiver clock (satellite clock bias). This means the receiver must have lock on at least 4 satellites at the same time to solve all the variables and determine a position. The range measurement is a function of time (𝑟 𝐶 ∆𝑡). The range measurement contains the clock bias. The distance to the satellite is referred to as the pseudorange because it is the range plus a clock correction term (∆r). 𝝆 𝒓 ∆𝒓 7|Page  5: Range vs pseudorange The fourth pseudorange is needed to solve for the clock bias. Historically, GPS receivers use the C/A code on the L1 signal to retrieve the navigation message and start locking on the satellites. Each satellite is assigned to a channel where the receiver can continue to listen to the signal and determine a range. Once the receiver determined a range of two different satellites, the processor unit in the receiver can begin determining the clock bias. Once the pseudorange to four satellites is found, a code pseudorange position can be solved. This code pseudorange has an expected precision of +/-10m. Modern GNSS receivers can use several different combinations of signals to acquire satellite (L2C code in the L2 signal for example), and do not specifically need the C/A code of the L1 signal. Pseudorange Equation Satellite Clock bias is one of the errors in the pseudorange measurement. Pseudorange is expressed by the following equation (Langley, 1993): 𝜌 𝑅 𝑐 𝑑𝑡 𝑑𝑇 𝑑 𝑑 𝜀 𝜀 Where:  ρ = the pseudorange measurement  R = the true range  c = the speed of causality  dt = the satellite offset from GPS time (satellite clock error) 8|Page   dT = The receiver offset from GPS time (satellite clock bias)  dion = ionospheric effects (upper atmosphere)  dtrop = tropospheric effects (lower atmosphere)  εmp = Errors from multipath  εp = Other error terms (receiver noise, etc.) Satellite Clock Bias, dt Satellite clock bias is the correction for satellite clock errors. Each satellite clock has its own clock correction bias. Individual satellite clocks are monitored as part of the control segment and individual satellite clock bias corrections are added to the navigation message. There is also a relativistic effect to be considered as well for satellites in orbit that is considered in the clock bias. The clock bias is extracted from the navigation message and applied to the pseudorange equation. Satellite clock bias is the largest item in the error budget. Receiver Clock Bias, dT As mentioned above, the receiver clock error can be determined by comparing simultaneous range measurements from two satellites. Since the dT value is the same in both range measurements, differencing the two equations will solve for the dT value. 𝜌 𝑅 𝑐 𝑑𝑡 𝑑𝑇 𝜌 𝑅 𝑐 𝑑𝑡 𝑑𝑇 𝜌 𝑅 𝑅 𝑐 𝑑𝑡 Ionospheric Effects, dion The satellite signals do not propagate in a vacuum. The signal must travel through the atmosphere before reaching the receiver. The various layers of the atmosphere diffract and refract the GNSS signals altering both the speed and direction of the signals. These time delays have a large affect on the pseudorange measurements. The Ionosphere is part of Earth's upper atmosphere, which varies between 80 and about 600 km. Extreme UltraViolet (EUV) and x-ray solar radiation ionizes the atoms and molecules thus creating a layer of highly charged electrons (plasma). The thickness, or density, of the ionosphere varies depending on the amount of EUV and radiation occurring at the moment. During the day, when the earth is facing the sun, the ionosphere is experiencing more solar radiation, and the ionosphere becomes more dense. At night, when Earth is facing away from the sun, the ionosphere is less dense. Same is true when the sun expels more radiation during solar storms, or other times of solar activity. The increased radiation excites the plasma of the ionosphere, and the plasma densifies. The density of the ionosphere is measured by a Total Electron Count (TEC), a measure of the number of free electrons in a column through the ionosphere having a cross-sectional area of exactly 1 meter. 9|Page  6: Model of the Ionosphere The error introduced by ionospheric effects varies based on several factors, including the time of day, solar activity, and the altitude angle of the satellite signal being received. Magnitude of ionospheric effects can reach as much as +/-150 meters on the individual satellite pseudorange and is the second largest contributor to the pseudorange error budget. Ionospheric affects different frequencies in different magnitudes. Frequency dependence of the ionospheric effects can be expressed by the following equation (Klobuchar, 1983): 40.3 𝑣 𝑇𝐸𝐶 𝑐𝑓 Where:  v = ionospheric effects  c = the speed of causality  f = signal frequency  TEC = number of free electrons per cubic meter Time delay is inversely proportional to the square of the frequency, meaning that higher frequency has a higher delay. And the effect is different for each frequency. The use of multiple frequencies (L1, L2, L5, etc.) is used to calculate and reduce the ionospheric effects term in the pseudorange equation. 10 | P a g e Tropospheric Effects, dtrop The troposphere is the lower portion of the atmosphere, which contains both the Tropopause and the Stratosphere. Tropospheric effects are independent of frequency, all GNSS signals are affected similarly. Like ionospheric effects, density of the troposphere at the moment of observation determines the magnitude of the effects. Tropospheric effect is comparable to atmospheric refraction in astronomic observations, and the effect increases the longer the distance of travel through the troposphere. Satellite elevation angle determines the extent of the tropospheric effect. The lower the satellite is on the horizon, the longer the signal path and the greater the tropospheric effects. The satellite signal path, and tropospheric effects, are at a minimum at zenith. Tropospheric effect is modeled using a wet and dry component. The dry component is the largest contributor to signal effects and is closely correlated to the atmospheric pressure. This makes the dry component easy to model. Wet portion of the model is measured using water vapor radiometers, which are used only in the highest precision applications. The practical consequence of the tropospheric effects is that the atmosphere is not homogeneous. Receivers working within a close proximity of each other will likely see similar atmospheric conditions. Those further away from each other will see a greater variation. Multipath Multipath is the result of the GNSS signal being reflected. Multipath occurs when the signal reflects off the ground, buildings, or other surfaces before reaching the receiver. 7: Multipath 11 | P a g e Several methods are used to mitigate the effects of multipath. Geodetic grade GNSS antennas have a grounding or base plate (also called a choke ring) which block signal reflected off the ground from reaching the antenna. 8: Choke Ring GNSS signals are also right hand polarized, meaning that they travel in a counterclockwise spiral. Reflected signals change polarity or spin the opposite direction. Higher grade antennas reject signals that are not right-hand polarized. 9: Right-hand polarization 10: Left-hand vs Right-hand polarization. 12 | P a g e Orbital Bias The broadcast ephemeris provides near future predictions of satellite position and attitude. These predictions allow the receiver to determine the satellites relative position at any given moment. However, these are predictions and are estimated based on monitoring by the control segment. The control segment updates the information daily, as the prediction diverges from the solution with time. Satellite orbits are disturbed by several different forces, such as nonspherical nature of Earth gravity, the gravitational forces of the sun and moon, pressures of solar radiation, as well as obstructions and friction from dust and other particles in space (space is not a vacuum). Every GNSS satellite is tracked and constantly monitored. The orbital tracking data is gathered to create a new ephemeris. Updated ephemeris showing the “true” location of the satellites are provided for higher precision in post-processing. However, the broadcast ephemeris is what is used in real-time. 11: Orbital error. Relativity Earth’s gravitational field creates relativistic affects on satellite orbits, signals and clocks that also need to be considered. Details on relativity are not discussed here but understand that corrections for these effects are considered and included as part of the navigation message. Antenna Phase Center Offset A GNSS antenna collects, filters, and amplifies incoming satellite signals which are sent to the receiver for processing. The antenna creates an electro-magnetic field around itself, and as the signals contact this field they are received and passed off to the filters and amplifiers within the circuit. This field is variable, dependent on elevation, altitude, and strength of the incoming signals. The mean of these reception points is used to define the physical location where the satellite signal is received by the antenna. This is referred to as antenna phase center (APC). APC 13 | P a g e is used to relate the position solution to a physical location. APC is generally calibrated and provided by the manufacturer. 12: General parts of a GNSS Antenna. Generally, this is applied to vertical component of the solution to relate the position to a reference point on the antenna (antenna reference point (ARP)) which is applied to the height of the instrument. However, the APC is not typically aligned with the physical center of the antenna. Antenna phase center variation (PCV) is defined as the deviation of the APC to the ARP. There is also a variation between the APC for each frequency (𝐴𝑃𝐶 𝐴𝑃𝐶 ), however only one mean APC value is used for any one antenna model to be applied to all incoming signals. These phase center variations can cause errors in high precision surveying. 13: PCV in relationship to APC and ARP. 14 | P a g e Carrier Phase Ranging The carrier phase measures the phase of the received carrier wave of the satellite signal with respect to the carrier phase generated in the receiver at the time of reception. It represents a measurement of the distance between satellite and receiver in cycle units of the carrier frequency. The observed measurement is obtained by shifting the generated signal carrier phase to match it with the received carrier phase from the satellite. Carrier phase measurements are generally much more precise than code pseudorange measurements since it can be tracked by a division of one wavelength and can provide a precision in the magnitude of millimeters. Wavelength is determined by the frequency of the signal: 𝑐 𝜆 𝑓 Where:  λ = wavelength  c = the speed of causality  f = signal frequency For the L1, 1575.42 MHz carrier frequency, the wavelength is approximately 19 cm. For L2, 1227.60 MHz carrier, the wavelength is approximately 24 cm. For L5, 1176.45 MHz carrier, the wavelength is approximately 26 cm. 𝑐 299.8 10 𝑚/𝑠𝑒𝑐 𝜆 ≅ 0.19𝑚 𝑓 1575.42 𝑀𝐻𝑧 𝑐 299.8 10 𝑚/𝑠𝑒𝑐 𝜆 ≅ 0.24𝑚 𝑓 1227.60 𝑀𝐻𝑧 𝑐 299.8 10 𝑚/𝑠𝑒𝑐 𝜆 ≅ 0.26𝑚 𝑓 1176.45 𝑀𝐻𝑧 The carrier phase measurement works in a similar fashion in an EDM. The EDM send a modulated carrier wave, and the receiver generates a similar wave as an internal reference. When the reflected EDM signal returns, the receiver generated phase signal is compared to the returned signal to determine the fractional piece of full wavelength that is remaining. The GNSS receiver works in a similar way, comparing the fractional piece of the wave to the receiver generated wave. However, the number of complete wavelengths is unknown. This unknown integer of “full wavelengths” is referred to as Integer Ambiguity. 15 | P a g e  14: Carrier phase measurement. Integer Ambiguity Because one cycle of the carrier phase signal is indistinguishable from another, the total number of cycles is ambiguous. Once this ambiguity is resolved, the receiver only needs to keep a count of how many whole number (integer) cycles there are between the satellite and receiver to keep a lock on the satellite. Once the receiver loses count, the lock with the satellite is lost (cycle slip). The carrier phase range can be determined to the millimeter level once the integer ambiguity is resolved. The high precision range determinations allow for sub-millimeter position solutions. Determining the integer ambiguity is difficult problem, especially trying to resolve these ambiguities quickly. Several complicated mathematical methods are used to quickly resolve the integer ambiguity and attain lock on as many satellites as possible. Carrier Phase Range Equation Carrier Phase observations are expressed by the following equation (Langley, 1993): 𝛷 𝑅 𝑐 𝑑𝑡 𝑑𝑇 𝜆𝑁 𝑑 𝑑 𝜀 𝜀 Where:  𝜱 = the carrier phase measurement  R = the true range  c = the speed of causality  dt = the satellite offset from GPS time (satellite clock error)  dT = the receiver offset from GPS time (satellite clock bias)  λN = Integer ambiguity  dion = ionospheric effects (upper atmosphere) (NOTE: NEGATIVE!)  dtrop = tropospheric effects (lower atmosphere)  εmp = Errors from multipath  ε𝜱 = Other error terms (receiver noise, etc.) 16 | P a g e Ionospheric Effects, dion The satellite signals do not propagate the same way for the code as the actual carrier wave. Ionospheric interactions affect the code modulations different than the carrier wave. These two effects are known as group delay and phase delay. Group delay is the apparently slowing of the modulated code. Phase delay is the apparent “speeding up” (negative delay) of the carrier wave. Point Positioning A GNSS receiver can determine its position by determining the simultaneous ranges to at least four satellites. As mentioned earlier, four satellites are needed to solve for the four unknowns in the user’s position, the 3D coordinates, and the receiver clock bias (UX, UY, UZ, dT). 17 | P a g e These same equations are applied to each epoch of measurement to determine an instantaneous position, allowing for the receiver to be in motion during measurement (kinematic positioning). Information within the navigation message allow the receiver to resolve some of the error factors (ionosphere and troposphere effects, satellite clock errors, orbital errors) with precision at the meter to tens of meters level (depending on observation length). Longer, stationary observation times (static positioning) will provide a stronger solution. Absolute Positioning Absolute positioning is using one receiver to determine position directly from satellites. Simpler satellite navigation systems, like those found in an automobile or cell phone, use the code pseudoranges to determine an absolute position in real time. Survey grade receivers use a combination of code and carrier phase measurements to determine a position with a much higher level of precision. The level of precision attainable from absolute positioning is dependent on the length of observation (number of observation epochs) and the processing tools used to resolve the various error factors in the observation equations. Precise Point Positioning Precise Point Positioning (PPP) is a post-processing technique that correction data compiled from a network of global reference stations to model and remove errors from the GNSS observations. PPP solutions require extended observation time to converge to a solution at the decimeter level, but solutions at the 1-3 cm level are attainable with very long observations. Errors in the PPP solution are mitigated using various methods. Ionospheric effect is dependent on the signal frequency. Combining the dual-frequency measurements can eliminate the first-order ionospheric effects. Satellite orbit and clock corrections are compiled from reference receivers and applied to the processing. Tropospheric delays are handled using modeling of the dry portion of the delay. Wet portion of the Tropospheric delay is difficult to model as it is dependent on the specific weather at the receiver location. PPP uses extended Kalman filtering to mitigate any noise in the signals. Canadian Spatial Reference System Precise Point Positioning (CSRS-PPP) There are several services available for providing a PPP processing, both public and private. Natural Resources Canada (NRCan) provides a variety of geodetic tools, including the Canadian Spatial Reference System Precise Positioning Service (CSRS-PPP): https://webapp.csrs-scrs.nrcan- rncan.gc.ca/geod/tools-outils/ppp.php. According to the NRCan website: CSRS-PPP is an online application for global navigation satellite systems (GNSS) data post- processing. It uses precise satellite orbit, clock and bias corrections derived from a global 18 | P a g e  network of receivers to determine accurate user positions anywhere on the globe, regardless of proximity to reference stations. Submit Receiver INdependent Exchange (RINEX) format observation data from single or dual-frequency receivers operating in static or kinematic mode over the Internet, and recover enhanced positioning precisions in the North American Datum of 1983 of the Canadian Spatial Reference System (NAD83(CSRS)) or the International Terrestrial Reference Frame (ITRF). RINEX Format RINEX is a Receiver INdependent data EXchange transfer format for GNSS observation data. Observation data is stored as three ASCII files: an observation data file, the navigation message, and a meteorological message. Almost all GNSS receiver manufacturers provide tools for providing RINEX data output. The format was originally designed for GPS data in 1989 and has been revised in a few iterations to include GLONASS, Galileo, and BeiDuo data. As of July 2023, the latest version of RINEX is 4.00. File naming convention for RINEX is as follows: ssssdddf.yyt Where:  ssss = station identifier  ddd = GPS day  f = file sequence number o generally, a letter referring to hour of the day, where a = 0:00 GST  yy = last two digits of the year o i.e. 24 for 2024  t = files type o o = observation file o n = GPS navigation file o m = meteorological file o g = GLONASS navigation file RINEX data is an ASCII format making it easy to use and edit. However, processing of the observation data using specialized software is required. Relative Positioning One method for removing errors, unknowns, and improving accuracy and precision, is the use of two or more receivers. The correlation between the simultaneous observations of identical observables allows for comparison of data and removal of certain common errors. For example: observing the same satellite from two different receivers at the same time removes the satellite clock error (dt). The two receivers are relatively close to each other compared to the distance to the satellites, so many of the common errors cancel out. Dependent on the baseline length of the two receivers, tropospheric and ionospheric effects will also likely be similar at both receivers. 19 | P a g e These correlated errors can be mitigated by the simultaneous observations and can provide a baseline measurement of +/- (1cm + 2ppm). Multiple receivers can be utilized to create a closed network of baseline vectors and provide millimeter level precision. This relative positioning method is often referred to as Differential GNSS (DGNSS, or DGPS). 15: Relative GNSS Positioning Static GNSS Surveying Static Surveying is a relative positioning technique that utilizes two or more stationary GNSS receivers simultaneously observing the same satellites. Typically, a base receiver is set up over a “known” control point (generally a monument, or control point). The remote receiver, or rover receiver, is setup on a second point of unknown position where it collects data for an extended period. The long the period, the more simultaneous observations are collected usually resulting in a stronger solution. Once all the observations are made for the prescribed period, the data is downloaded and processed to determine the baseline vectors between the base receiver and the rover locations. These baseline vectors can then be combined to create a network of vectors which can be least squares adjusted to provide position solutions for each rover location. Kinematic GNSS Surveying Kinematic Surveying is a relative positioning technique that utilizes two or more GNSS receivers simultaneously observing the same satellites. Like static methods, a base receiver is typically set 20 | P a g e up over a “known” control point (generally a monument, or control point), while the rover receivers are in motion. The remote receiver, or rover receiver, is setup on a second point of unknown position where it collects data for a short period of time. The rover receiver can also be tracked while in motion to create a trajectory. For mapping purposes, the rover generally stops at a point of interest to collect data in brief static setups. The collected data can be post- processed to solve the baseline vectors and static points (post-processed kinematic, PPK). The base and rovers can also communicate via radio, or internet, to provide correction data and process the vectors in real-time (real-time kinematic, RTK) to give point position solutions on the fly. 16: Real-Time Kinematic, RTK. Correction data from a GNSS base can also be provided by real-time networks (RTN) via the internet. There are several subscription RTN services available from various manufacturers and municipalities. These networks allow user to log into a network of constantly operating base stations to receive real-time corrections for RTK GNSS data collection. These networks add the convenience of not having to setup a base station, being restricted by radio communication, and provide robust error corrections for improved performance. Most network RTK systems utilize a communications protocol known as Network Transport of RTCM via Internet Protocol (NTRIP) to provide instantaneous correction data to the rover. RTCM Format Radio Technical Commission for Maritime Services (RTCM) define a universal data format for real- time transmission of GNSS correction data from base receivers to rover receivers. This format is optimized to provide GNSS information between receivers of any make or model, for universal use. 21 | P a g e Manufacturers also have their own proprietary data formats for corrections data as well that can provide more information and improve individual performance (i.e. TrimTalk or Leica 4G). These formats are generally not compatible with other manufacturers’ equipment. Coordinate Systems in GNSS Map Projections Most of traditional surveying data relates measurements to a map, or plan. This works to relate real world measurements to a planar surface over a small area, where the curvature of the Earth has minimal effect over the field measurements. Relating measurements over much larger area, or the entire globe, creates distortions in both size and shape. Large area surveys are limited in a horizontal plane datum, requiring the stretching and/or compressing of the data to best represent a curvature while minimizing distortions. To best express Geodetic considerations of a curved Earth while minimizing map distortions, conical, cylindrical, or azimuthal (planar) projections are used to uniformly express curved features on a flat surface. The conical, cylindrical surfaces at tangential to the surface along a line (Central Meridian). Planar surfaces are tangential to the surface at a specific point (Point of Tangency). 17: Cylindrical, Conical, and Azimuthal map projections of a sphere. Azimuthal Map Projections preserves distances, and azimuths while distorting the shapes of the projection. Conical Map and Cylindrical Projections, such as Lambert Conformal Conic Projection and Transverse Mercator Projections, are commonly used for State and Provincial plane coordinate systems. Conical and cylindrical projections preserve azimuth and shapes while distorting (scaling) the distances. 22 | P a g e  18: Conical, Cylindrical, and Planar map projections. The project area generally dictates which projection will work best to express the details of the area while minimizing the distortions of size and shape. In North America, there are State and Provincial wide plane coordinate systems to relate local work to the mapping plane. Each coordinate system is defined by the State or Provincial governing body and uses a projection that best fits the area of interest with minimal distortions. These State and Provincial systems help coordinate projects and minimize Geodetic calculations. 3D Cartesian Coordinates Geodetic coordinate systems relate geographic locations in angular coordinates (longitude, latitude) as defined by a particular datum. Geodetic coordinates use a curvilinear orthogonal coordinate system that is based on a reference ellipsoid. Ellipsoidal height (h), or elevation of the location, is treated as an induvial component. 3D Cartesian Coordinates relate geographic locations in three rectangular coordinates (X,Y,Z) to a reference ellipsoid with the origin (0,0,0) at that ellipsoid’s center. Cartesian coordinates allow for height to be included as part of the system and not an individual component. A Conventional Terrestrial Reference System (CTRS) is a 3D cartesian coordinate system with the origin located at the Earth’s center of mass (geocenter). X-axis is defined as a line extending from the geocenter 23 | P a g e to the intersection of the prime meridian and the equator. Y-axis is defined as perpendicular to the x-axis in the same equatorial plane. Z-axis is a line extending through the geocenter, and perpendicular to the equatorial plane (Conventional Terrestrial Pole). This is also referred to as an Earth-Centered-Earth-Fixed Coordinate System (ECEF). 19: Earth-Centered-Earth Fixed Coordinate System. Polar Motion Earth rotates about its rotational axis. This periodic rotation of the Earth’s rotational axis causes Earth to wobble. The variations between Earth's instantaneous rotational axis, and the Conventional Terrestrial Pole are referred to as Polar Motion. The gravitational forces of the sun and moon cause the Earth to wobble about its rotational axis. These forces affect the Earth in two well defined motions, precession, and nutation. Precession is the greater of the two motions, which is the wandering of the instantaneous pole from the Conventional Terrestrial Pole. The cycle of precession is about 26,000 years. Nutation is the smaller motion of the of rotation about the processional arc. These nutation rotations have a period of about 18.6 years. The location of the CTP was initially defined as the mean position of the instantaneous pole between the years 1900 and 1905. 24 | P a g e  20: Precession (P) and Nutation (N). International Earth Rotation Service (IERS) (https://www.iers.org/) monitors the instantaneous position of the pole with respect to the CTP since 1988. Very Long Baseline Interferometry and Lunar Laser Ranging. CTS is currently defined by instantaneous spatial coordinates of a set of monitoring stations around the globe known as the International Terrestrial Reference Frame (ITRF). ITRF is used in the computation of precise orbits and is referenced by time-dependent models to other coordinate systems. The instantaneous position of the pole with respect to the CTP is used for the reduction of astronomical azimuths, and can be applied using the relationship: 𝐴𝑧 𝐴𝑧 𝑥 sin 𝜆 𝑦 cos 𝜆 sec 𝜙 Where:  AzAstro = Astronomic Azimuth with respect to the CTP  AzObserved = Observed Azimuth with respect to the instantaneous pole  (x,y) = coordinates of the instantaneous pole  (ϕ,λ) = geodetic latitude and longitude of the observing station Ellipsoidal Model An ellipsoidal model is a mathematical surface defined as an ellipse revolved around Earth’s polar axis. The dimensions of the ellipse are chosen to best mathematical fit the physical earth. Different reference ellipsoids mathematically fit specific areas of the earth better than others. Size and shape of the ellipsoid are defined by two parameters: length of the semi-major axis (a) and flattening (f). Flattening is a ratio of the lengths of the semi-major (a) and semi-minor (b) axes of the ellipsoid: 25 | P a g e  𝑏 𝑓 1 𝑎 21: Ellipsoidal model of Earth. Geoid Model The geoid is an equipotential gravitational surface on which every point is perpendicular to the direction of gravity. Due to Earth’s uneven distribution of mass, and irregular rotation, the geoid is an irregular shape. The Geoid contains nonuniform undulations and is not easily defined mathematically. The Geoid represents a common gravity potential, or elevation that is used as a datum to represent the surface of the Earth. Geoid models are used to relate the surface of the geoid to a reference ellipsoid. 22: Earth, ellipsoid, and the geoid. 26 | P a g e Different ellipsoidal models fit the geoid better in specific locations better than others. For example, the Clarke 1866 Ellipsoid Model was used to define reference systems in North America due to its closeness of mathematical fit to the geoid locally. However, satellite positioning requires an ellipsoidal model that best fits the entire globe. 23: The geoid and two different ellipsoids. Geoidal Undulation The geoid is a representation of a continuous surface of equal gravity potential. Is considered a datum for elevation above or below the surface of the earth. An ellipsoid is chosen to best fit the geoid and ease the calculation and determination of a position on the Earth. As previously stated, receiver and satellite positions are defined by 3D cartesian coordinates (X, Y, Z) about a reference ellipsoid. The receiver elevation is defined by its position above the reference ellipsoid, or ellipsoidal height (h). Real world elevation, or an elevation based on sea-level, is an elevation above the geoid, or orthometric height (H). The difference between these two values is known as geoidal undulation (N), defined by the relationship: 𝐻 ℎ 𝑁 24: Ellipsoidal Height (h), Geoidal Height (H), and Geoidal Undulation (N). 27 | P a g e Deflection of the Vertical As stated earlier, all points on the geoid are perpendicular to gravity. However, all points on the ellipsoid a normalized, in that all points are a radial from a geometrically defined center. Points on the ellipsoid are not necessarily align with respect to gravity. The angular difference between these two directions is referred to as deflection of the vertical. Relating differences between the projection of the receiver location to the geoid and ellipsoid is required to properly reduce the observed azimuth to astronomic azimuth. 25: Deflection of the vertical. GRS80 and WGS84 Ellipsoids Global Reference System 1980 (GRS80) is global geocentric reference system was adopted in 1979. The reference system outlines several parameters of the Earth model, including (but not limited to) reference ellipsoid, gravitational velocity, magnetic field model, and angular velocity. It is uses the GRS80 ellipsoid as a reference surface that is a best fit to the geoid model. GRS80 ellipsoid is defined by a semi-major axis (a) of 6378.137 km, and a flattening (f) of 1/298.25722. GRS80 is a standard in North American reference system, and a basis of North American Datum 1983 (NAD83). the World Geodetic System 1984 (WGS84) is a global reference system that uses the WGS84 ellipsoid as a reference. WGS84 only slightly from GRS80, the origin is shifted and the shape is slightly different (see table below). WGS84 was optimized to best fit a global Earth. GPS uses WGS84 as a reference ellipsoid. 28 | P a g e  Ellipsoid Semi-major axis a Semi-minor axis b Inverse flattening 1/f GRS80 6378137.0 m ≈ 6356752.314140 m 298.257222100882711... WGS84 6378137.0 m ≈ 6356752.314245 m 298.257223563 GNSS measurements and position solutions (X,Y,Z) are related to positions on the WGS84 ellipsoid. GNSS (X,Y,Z) coordinates need to be related to actual geometric locations. Horizonal position needs to be projected to a map, and the ellipsoid elevations need to be related to a geoid. Choosing the right map projection and geoid model is dependent on what system is used in the local area. Because GNSS data works on a global system, the 3D cartesian data can be related to whatever map projection and datum needed. Time Systems There is also the standardization of time that is crucial for the reference frame. Time is a measure of Earth’s rotation, using the unit hour angle to denote a displacement between the current meridian, or the meridian of a celestial body, to a reference meridian (Greenwich meridian). Universal Time (UT) (or Solar Time) is defined as the hour angle from the Greenwich meridian, augmented by 12 hours (Sun crosses Greenwich at noon rather than midnight), by a fictious sun in an orbital plane at a constant angular velocity. Sidereal Time is defined as the hour angle attended from the vernal equinox. Solar Time is related in the terms that the sun returns its highest altitude at noon each day. Sidereal time is related to the Earth making a full 360° rotation each day. 26: Sidereal vs Solar Time. 29 | P a g e Earth’s rotational velocity (ωE) is defined by the WGS84 reference system as: 𝜔 72.92115 10 rad/s Angular velocity is defined as a uniform rate. Earth’s rotation is not uniform. This requires satellite positioning systems to rely on sidereal time measurement to account for natural irregularities in Earth’s rotation. Dynamic Times are derived from planetary motions, and serves as the basis for determining satellite attitude, and orbital irregularities. Universal Coordinated Time (UTC) is a dynamic time system using atomic clocks to coordinate satellite clock time with UT and Earth’s rotational irregularities. Integer leap-seconds are introduced as needed to coordinate UTC with local solar time. 30 | P a g e