GNSS Fundamentals

Overview#

Global Navigation Satellite System (GNSS) is the umbrella term for all satellite-based positioning systems. GPS is the most well-known, but it is only one of several fully operational constellations. Modern survey-grade receivers track satellites from multiple constellations simultaneously, improving availability, geometry, and reliability -- particularly in obstructed environments where a single constellation may not provide sufficient satellite coverage.

"GNSS is a generic term for satellite navigation systems that provide autonomous geospatial positioning with global coverage. It includes GPS, GLONASS, Galileo, BeiDou, and other regional systems." -- Van Sickle, GPS for Land Surveyors (4th Ed.), Ch. 1, p. 3

Understanding GNSS fundamentals begins with three questions: What is in orbit? What controls the system from the ground? And how does a receiver on the Earth's surface use the signals to compute a position?

The Three Segments#

Every GNSS constellation is organized into three segments: the space segment, the control segment, and the user segment. This architecture is common across GPS, GLONASS, Galileo, and BeiDou.

Space Segment

The space segment consists of the satellite constellation itself. For GPS, this is a nominal constellation of 24 satellites (with operational spares bringing the total to 31 or more) arranged in six orbital planes, each inclined at 55 degrees to the equator. The orbital altitude is approximately 20,200 km, giving each satellite a period of about 11 hours and 58 minutes -- just under half a sidereal day. This means the satellite geometry repeats approximately 4 minutes earlier each day.

"The GPS satellite constellation was designed so that at least four satellites are always visible from any point on the Earth's surface at any time." -- Ghilani & Wolf, Elementary Surveying (13th Ed.), Ch. 14, p. 387

Control Segment

The control segment consists of ground-based facilities that monitor satellite health, track orbits, update navigation messages, and synchronize satellite clocks. For GPS, the master control station is at Schriever Space Force Base in Colorado Springs, supported by a network of monitor stations distributed around the globe and ground antennas that upload corrections to the satellites.

The control segment performs several critical functions:

• Orbit determination. Monitor stations continuously track all satellites and compute precise orbital parameters (ephemerides).
• Clock synchronization. Satellite atomic clocks are monitored and corrections are computed and uploaded so that each satellite broadcasts its clock offset relative to GPS system time.
• Health monitoring. Satellites that malfunction or deviate from acceptable parameters are flagged as unhealthy in the navigation message so that receivers can exclude them.

User Segment

The user segment comprises all GNSS receivers -- from the survey-grade dual-frequency receiver on a tripod to the chip in a smartphone. The receiver's job is to acquire satellite signals, measure the pseudoranges (and, for survey receivers, the carrier phase), decode the navigation message, and compute a position solution.

The GPS Constellation in Detail#

GPS (officially NAVSTAR GPS) is operated by the United States Space Force. It was declared fully operational in 1995 and has been the backbone of satellite positioning for land surveying ever since.

The six orbital planes are identified by letters A through F. Each plane is separated by 60 degrees of right ascension. Within each plane, satellites are spaced unevenly (not equally distributed) to optimize global coverage and minimize the probability of poor satellite geometry at any given location and time.

How Positioning Works#

Trilateration and Pseudoranges

The fundamental concept behind GNSS positioning is trilateration -- determining a position by measuring distances from known points. Each satellite broadcasts its position (via the navigation message) and a timing signal. The receiver measures the time it takes for the signal to travel from the satellite to the receiver and multiplies by the speed of light to obtain a distance -- the pseudorange.

The basic pseudorange equation is:

$P = \rho + c \cdot (dt - dT) + d_{\text{iono}} + d_{\text{tropo}} + \epsilon_P$

where:

• $P$ is the measured pseudorange
• $\rho$ is the true geometric range from satellite to receiver
• $c$ is the speed of light ($\approx 299{,}792{,}458 \text{ m/s}$)
• $dt$ is the receiver clock error
• $dT$ is the satellite clock error
• $d_{\text{iono}}$ is the ionospheric delay
• $d_{\text{tropo}}$ is the tropospheric delay
• $\epsilon_P$ is measurement noise and other unmodeled errors

The geometric range itself is:

$\rho = \sqrt{(X_s - X_r)^2 + (Y_s - Y_r)^2 + (Z_s - Z_r)^2}$

where $(X_s, Y_s, Z_s)$ is the satellite position and $(X_r, Y_r, Z_r)$ is the unknown receiver position.

Why Four Satellites?

Three distance measurements from three satellites with known positions would theoretically fix a point in three-dimensional space. However, the receiver clock is not synchronized to GPS system time -- it uses an inexpensive quartz oscillator rather than an atomic clock. This clock error introduces a fourth unknown. Therefore, a minimum of four satellites must be observed simultaneously to solve for the four unknowns: $X_r$, $Y_r$, $Z_r$, and $dt$.

"Because the receiver clock is not synchronized with GPS time, four satellites are required: three to determine position and one to determine the receiver clock error." -- Van Sickle, GPS for Land Surveyors (4th Ed.), Ch. 3, p. 67

In practice, modern multi-constellation receivers routinely track 15--25 satellites at once, providing redundant observations that strengthen the solution and allow the receiver to detect and exclude problematic measurements.

Dilution of Precision#

The geometric arrangement of observed satellites directly affects the quality of the position solution. This effect is quantified by the Dilution of Precision (DOP) -- a dimensionless scalar that multiplies the measurement error to produce the position error.

$\sigma_{\text{position}} = \text{DOP} \times \sigma_{\text{range}}$

A lower DOP indicates better satellite geometry and a more precise solution. DOP values are categorized as follows:

PDOP is lowest when satellites are spread widely across the sky. Satellites clustered in one part of the sky produce high PDOP and weak solutions, particularly in the vertical component. VDOP is almost always larger than HDOP because satellites are only visible above the horizon, limiting the vertical geometric strength.

"DOP is strictly a function of satellite geometry. It is independent of signal quality, receiver performance, or atmospheric conditions." -- GEOG 862, GPS and GNSS for Geospatial Professionals, Penn State, Lesson 3

Single Point Positioning vs. Differential Positioning#

Single Point Positioning (SPP)

Autonomous or single-point positioning uses a single receiver processing pseudorange measurements with broadcast ephemerides and clock corrections. This is the mode used by handheld GPS units and smartphones. Accuracy is typically in the range of 3--5 meters horizontally (with no augmentation) and 5--10 meters vertically.

SPP is adequate for navigation and GIS data collection but falls far short of the centimeter-level accuracy required for professional land surveying.

Differential Positioning

Differential positioning is the foundation of all survey-grade GNSS work. It exploits the fact that many error sources -- satellite clock errors, orbital errors, ionospheric and tropospheric delays -- are spatially correlated. By placing a receiver at a known position (the base or reference station), the errors at that location can be computed and applied as corrections to the rover receiver operating nearby.

The key categories of differential positioning are:

• DGNSS (Differential GNSS). Code-based corrections applied to pseudoranges; accuracy of 0.5--2 meters.
• RTK (Real-Time Kinematic). Carrier-phase-based corrections transmitted in real time; accuracy of 1--2 cm + 1 ppm.
• Static / Post-Processed. Carrier-phase observations recorded at both base and rover, processed after the fact; accuracy ranges from sub-centimeter (static) to centimeter (kinematic).

The mathematical basis of differential correction is straightforward. If the base station's true position is known, the pseudorange error at the base can be computed:

$\delta P_{\text{base}} = P_{\text{measured}} - P_{\text{true}}$

This correction, applied to the rover's pseudorange for the same satellite at the same epoch, removes the spatially correlated error components. The effectiveness of the correction decreases as the baseline length increases, because the errors become less correlated over distance -- a phenomenon called spatial decorrelation.

"The fundamental principle of differential GPS is that the errors observed at a reference station can be used to correct the errors at a nearby user receiver, because the dominant error sources are spatially correlated." -- Ghilani & Wolf, Elementary Surveying (13th Ed.), Ch. 14, p. 398

Satellite-Based Augmentation Systems (SBAS)#

Satellite-Based Augmentation Systems improve the accuracy and integrity of single-point GNSS positioning by broadcasting differential corrections and integrity information via geostationary satellites. SBAS corrections are free to use and are automatically applied by most modern receivers.

SBAS improves autonomous positioning accuracy from approximately 3--5 meters to 1--2 meters horizontally. While this is insufficient for professional surveying, it is useful for navigation, GIS data collection, and as a crosscheck in the field. SBAS corrections do not replace differential carrier phase techniques for survey-grade work.

Coordinate Reference Frames#

WGS 84

The World Geodetic System 1984 (WGS 84) is the native coordinate reference frame of GPS. All GPS satellite positions in the broadcast ephemeris are expressed in WGS 84. A raw GPS position solution is therefore in WGS 84 coordinates -- typically given as geodetic latitude, longitude, and ellipsoid height.

The WGS 84 ellipsoid has the following defining parameters:

In its current realization (WGS 84 G2139), WGS 84 is aligned with ITRF2014 at the centimeter level. For practical purposes in modern surveying, a WGS 84 position is effectively an ITRF position.

ITRF

The International Terrestrial Reference Frame (ITRF) is the most accurate global reference frame, maintained by the International Earth Rotation and Reference Systems Service (IERS). Precise GNSS orbits from organizations like the International GNSS Service (IGS) are expressed in ITRF. When post-processing GNSS data with precise ephemerides, the initial solution is in ITRF and must be transformed to the working datum (e.g., NAD 83).

Because ITRF is an Earth-centered, Earth-fixed frame that accounts for tectonic plate motion, coordinates in ITRF change over time. A station on the North American plate moves approximately 1--2.5 cm per year relative to the geocenter. ITRF positions must therefore always be expressed at a specific epoch (e.g., ITRF2014, epoch 2020.0). The position at any other epoch is computed using the station's velocity vector:

$\mathbf{X}(t) = \mathbf{X}(t_0) + \dot{\mathbf{X}} \cdot (t - t_0)$

where $\mathbf{X}(t_0)$ is the position at the reference epoch, $\dot{\mathbf{X}}$ is the velocity vector, and $t - t_0$ is the elapsed time in years.

Practical Implications

For land surveyors in North America, the working datum is typically NAD 83 (in a specific realization such as NAD 83(2011), epoch 2010.0). The transformation from ITRF/WGS 84 to NAD 83 involves a 14-parameter Helmert transformation that accounts for the approximately 1--2 meter offset between the two frames plus the motion of the North American tectonic plate. Processing software handles this transformation, but the surveyor must ensure the correct datum and epoch are specified.

Comparison of Major GNSS Constellations#

The benefit of tracking multiple constellations is primarily increased satellite availability and improved geometry. In challenging environments -- urban canyons, forested areas, steep terrain -- a GPS-only receiver might see only 4--6 satellites with poor PDOP, while a multi-constellation receiver might track 15--20 satellites with excellent geometry.

"Multi-constellation receivers can track GPS, GLONASS, Galileo, and BeiDou simultaneously, significantly increasing the number of available satellites and improving position accuracy, particularly in environments with obstructed sky views." -- Ghilani & Wolf, Elementary Surveying (13th Ed.), Ch. 14, p. 391

Key Takeaways#

• GNSS is the umbrella term encompassing GPS, GLONASS, Galileo, BeiDou, and other satellite navigation systems. GPS is one constellation, not the whole system.
• Every GNSS constellation has three segments: the space segment (satellites), the control segment (ground monitoring and upload facilities), and the user segment (receivers).
• GPS uses 31+ satellites in 6 orbital planes at approximately 20,200 km altitude with a ~12-hour period.
• Positioning works by trilateration -- measuring pseudoranges from satellites with known positions. Four satellites minimum are required because the receiver clock error introduces a fourth unknown.
• Dilution of Precision (DOP) quantifies how satellite geometry affects position accuracy. Lower DOP means better geometry and more precise solutions.
• Single point positioning (3--5 m accuracy) is inadequate for surveying. Differential positioning (base + rover) is the foundation of all survey-grade GNSS work.
• GPS positions are natively in WGS 84, which at its current realization is effectively aligned with ITRF at the centimeter level. Working coordinates in North America are typically on NAD 83 (a plate-fixed datum offset ~1--2 m from ITRF/WGS 84).
• Multi-constellation receivers improve satellite availability, geometry, and reliability, especially in obstructed environments.

References#

1. Van Sickle, J. GPS for Land Surveyors (4th Ed.). CRC Press, 2015. Chapters 1--3.
2. Ghilani, C.D. & Wolf, P.R. Elementary Surveying: An Introduction to Geomatics (13th Ed.). Pearson, 2012. Chapter 14.
3. GEOG 862: GPS and GNSS for Geospatial Professionals. Penn State College of Earth and Mineral Sciences. Lessons 1--3.
4. National Coordination Office for Space-Based Positioning, Navigation, and Timing. "GPS.gov -- Official U.S. Government Information about GPS." https://www.gps.gov/
5. European Union Agency for the Space Programme. "Galileo -- European Global Navigation Satellite System." https://www.euspa.europa.eu/
6. International GNSS Service (IGS). "IGS Products." https://igs.org/products/