Scientific reference · Updated 30 September 2026
GNSS terms, units and the calculations behind them
Use this glossary while working through the numerical lessons. Each definition identifies a convention or unit that matters in an implementation and links directly to the corresponding calculation. Start with the guided learning route if the terms are new.
GNSS
Global Navigation Satellite System is the general term for satellite navigation systems. GPS is one constellation; Galileo, GLONASS and BeiDou are others. A GNSS receiver estimates position and time from satellite signals, with the model depending on the observables and products used.
GPS time (GPST)
A continuous time scale counted from 6 January 1980. GPS week and seconds-of-week identify an epoch. UTC conversion requires the offset valid at that epoch; a calendar timestamp must not be assumed to use GPS time merely because it came from a GNSS file.
RINEX
Receiver Independent Exchange Format stores GNSS observations and navigation records. Check the version, time system and observation-type order in the header before reading numerical fields. Observation files and navigation files serve different roles in the positioning chain.
Pseudorange
A code-based range observable that includes geometric distance, receiver and satellite clock effects, atmospheric delays and measurement error. It is not a direct geometric distance. A positioning model accounts for these terms before solving for the receiver state.
Carrier phase
The measured accumulated carrier phase contains a geometric range contribution, clock and propagation effects, and an unknown ambiguity. RINEX L observables are recorded in cycles; multiply by the signal wavelength to combine them with range terms in metres.
C1C and L1C
In RINEX 3 GPS observations, C1C is code pseudorange and L1C is carrier phase on the GPS L1 C/A signal. The C or L identifies the observable, while the remaining characters identify frequency and tracking attribute. Read the satellite system and header together.
ECEF
Earth-centered, Earth-fixed Cartesian coordinates rotate with Earth. X, Y and Z coordinates are used for satellite and receiver positions in the worked examples. Local horizontal and vertical uncertainties require transformation to ENU; the ECEF Z axis is not a station’s local up direction.
ENU
East, north and up form a local frame at a reference latitude and longitude. Rotating an ECEF position covariance into ENU makes horizontal and vertical uncertainty meaningful at that location. State whether coordinates are absolute positions or offsets from a local origin.
Broadcast ephemeris
Satellite navigation messages provide parameters for propagating an orbit and modeling the satellite clock over their validity interval. Select the record for the correct satellite, epoch and health state. The supplied orbital parameters must be propagated; they are not ready-made satellite coordinates.
toe and toc
toe is the reference epoch for the orbital model; toc is the reference epoch for the satellite clock model. Their roles differ even when the numerical values coincide. Evaluate time differences in the proper GPS week and apply week-crossover handling.
Signal transmission time
The signal left the satellite before it reached the receiver. Propagate the satellite state at transmission time using a travel-time estimate and consistent clock corrections. Reception-time coordinates alone introduce a modeling discrepancy in the computed range.
Earth rotation / Sagnac correction
Earth rotates while a signal travels from satellite to receiver. Satellite coordinates at emission and receiver coordinates at reception must be expressed consistently. The tutorials use an Earth-rotation correction in the geometric range calculation; apply the chosen convention once.
SP3 precise orbit products
SP3 files contain sampled precise satellite positions and optional clock values. Position fields use kilometres and clock fields use microseconds in the format. Interpolate the relevant samples, interpret missing-value flags, and convert to the working units explicitly.
Klobuchar model
The GPS broadcast ionospheric model estimates a single-frequency L1 code delay from broadcast coefficients, position, elevation, azimuth and time. The standard algorithm uses semicircles and a specified empirical slant factor. Follow IS-GPS-200 conventions rather than mixing mapping functions from other ionosphere models.
Saastamoinen model
A neutral-atmosphere delay model separates hydrostatic and wet contributions using atmospheric conditions and station geometry. Zenith delays require a mapping function for the slant path. A simple inverse-sine mapping is a teaching approximation, especially limited at low elevation.
Single point positioning (SPP)
SPP estimates an absolute receiver position and clock offset from code observations and satellite states. The worked GPS example includes orbit, clock, Earth rotation and atmosphere modeling before iterative weighted least squares. The result’s reliability depends on the observations, geometry and model.
Single difference
Subtracting same-satellite observations between two receivers cancels the common satellite-clock term under consistent modeling. Receiver-clock differences remain. Nearby receivers also share some propagation errors, although atmospheric and other effects do not cancel perfectly.
Double difference
Subtract a reference-satellite single difference from another satellite’s single difference. This removes the common receiver-clock difference. Observations that share the reference become correlated; differencing does not eliminate the carrier-phase ambiguities or every propagation error.
Baseline vector
A baseline is the coordinate difference between the two stations. This lesson defines b = base − rover, so its vector points from rover to base and rover = base − b. Other software may use the opposite sign; verify it before comparing results.
Reference satellite
The common satellite chosen for forming between-satellite differences. Reusing it couples the double-difference observations through its measurement error. A change of reference also changes the ambiguity basis, so ambiguity vectors cannot be compared without transforming their convention.
Design matrix
The design matrix contains derivatives of modeled observations with respect to the estimated parameters. In SPP it connects line-of-sight geometry to position and clock updates. In the relative model it also includes ambiguity columns; column units and parameter order matter.
Weighted least squares (WLS)
WLS estimates parameters by minimizing a residual quadratic form with the inverse observation covariance. Correlated double differences require a full covariance model. Whitening followed by QR solves the equivalent least-squares system without explicitly forming and inverting the normal matrix.
Covariance and correlation
Covariance describes model-based variances and dependencies. For observations transformed by D, propagate R_DD = D R_UD Dᵀ. A small formal covariance does not prove small actual error: unmodeled biases or incorrect weights may produce an overconfident estimate.
Residual
The difference between an observed quantity and its modeled value under the stated sign convention. Residual plots reveal inconsistency after estimation, but small residuals alone do not validate an ambiguity fix or detect every systematic error. Check the model, weights and independent diagnostics together.
DOP, PDOP, HDOP and VDOP
Dilution of precision describes geometry amplification under an assumed observation model. PDOP combines three position directions; HDOP and VDOP use local horizontal and up components. Classical DOP is dimensionless and cannot be read as a position error in metres without an observation-noise scale.
Float ambiguity
A real-valued estimate of a carrier-phase ambiguity before imposing the integer constraint. Float ambiguities and their joint covariance are inputs to integer least squares. Individual rounding ignores those correlations and may select the wrong joint candidate.
LAMBDA
Least-squares AMBiguity Decorrelation Adjustment transforms the ambiguity lattice with an integer-preserving unimodular transformation and searches for integer least-squares candidates. The original ambiguity basis and the transformed basis must use consistent vector and covariance conventions.
Ambiguity ratio test
A comparison of candidate objective values, often expressed as the second-best divided by the best value. Define that convention explicitly. A large separation favors one candidate in the assumed model, but the threshold is not a universal guarantee of a correct fix or accurate position.
RTK and PPP
RTK uses carrier-phase observations with a reference station or network to support relative precise positioning. PPP uses precise satellite products and an undifferenced absolute model. The published double-difference example is a single-epoch teaching computation, not a complete operational RTK service or a PPP implementation.
Check a definition against its source
The reference library links the GPS interface specification, IGS file formats, ESA explanations and ambiguity-resolution research. Our methodology explains the teaching assumptions and validation limits. Suggest a correction with the term and the convention you are using.