Foundations
GPS Time Conversion
A step-by-step numerical conversion from GPS-time calendar components to Julian Date and GPS seconds-of-week.
Fundamentals14 min
Tutorials
Numerical GNSS tutorials.
Tutorials are grouped by the learning path: foundations, files, satellite orbits, corrections, geometry, and positioning algorithms.
Module
Foundations
Time tags and the minimum coordinate context needed before reading GNSS files.
Coordinate systemsDirections, azimuth, and elevation
Module
Observations and Files
RINEX observation rows, navigation records, and precise orbit file anatomy.
RINEX Navigation BasicsSP3 File Basics
Observations and files
RINEX Observation Basics
A practical map of a RINEX 3 observation file, including headers, observation type codes, and epoch records.
Fundamentals16 min
Module
Satellite Orbits and Ephemerides
The orbit side of SPP: Keplerian elements, broadcast propagation, and SP3 interpolation.
Satellite position from multiple PRNs
Satellite orbits and ephemerides
Keplerian Elements in GPS Navigation Messages
A numerical map of GPS broadcast ephemeris fields: clock parameters, orbit shape, harmonic corrections, time references, and hardware delays.
Fundamentals20 min
Satellite orbits and ephemerides
Satellite Position from Broadcast Ephemeris
A step-by-step numerical satellite-position computation using broadcast ephemeris values from the legacy interpolation example.
Intermediate30 min
Satellite orbits and ephemerides
SP3 Interpolation
A numerical SP3 tutorial covering header records, epoch position rows, missing clocks, and Lagrange interpolation.
Intermediate26 min
Module
Corrections
Atmospheric and hardware corrections that turn raw code ranges into a cleaner model.
Collins tropospheric model
Corrections
Klobuchar Ionospheric Correction
A numerical Klobuchar walkthrough from receiver/satellite geometry to L1 delay in meters.
Intermediate22 min
Corrections
Saastamoinen Tropospheric Delay
A Tehran-based numerical example for standard atmosphere parameters, zenith delays, slant mapping, and final tropospheric range delay.
Intermediate24 min
Module
Geometry and Quality
Satellite geometry, error amplification, covariance, and practical accuracy interpretation.
GPS accuracy and error sourcesMultipath
Geometry and quality
ECEF to ENU: Coordinates and Covariance
A reproducible ECEF to ENU numerical example: subtract the local origin, construct the rotation, propagate covariance and interpret horizontal and vertical uncertainty.
Intermediate20 min
Geometry and quality
DOP Calculation
A design-matrix view of dilution of precision, with formulas and a compact numerical covariance example.
Intermediate18 min
Module
Positioning Algorithms
The complete numerical path from observations and navigation data to a receiver solution.
Positioning algorithms
SPP from Scratch
Compute GPS single point positioning from RINEX observations: transmission time, satellite clocks, broadcast orbits, Sagnac and atmospheric corrections, iterative WLS, residuals and covariance.
Intermediate150 min
Module
Advanced Positioning
Carrier-phase ambiguity resolution and precise positioning after the SPP foundation.
PPPPPP-ARCycle Slip Detection
Published advanced tutorial
LAMBDA Method
Integer ambiguity decorrelation and search for high-precision carrier-phase GNSS.
Published advanced tutorial
Double Difference from Scratch
Trace real RINEX observations through single and double differences, covariance, QR weighted least squares, LAMBDA and a candidate-fixed baseline.