Navigation from First Principles
A sequential tutorial series. These posts are meant to be read in order, from foundations through GNSS, inertial navigation, and full fusion.
A 27-part tutorial sequence from core concepts through GNSS, inertial navigation, filtering, outages, and final fusion.
- Part 1
What Does Navigation Actually Mean?
Introduce navigation as state estimation: position, velocity, attitude, time and uncertainty.
- Part 2
Coordinates and Frames: Describing a Place Precisely
Explain latitude, longitude, height, ECEF and local navigation frames.
- Part 3
True North, Magnetic North, Heading, Bearing and Course
Explain heading, bearing, course over ground and magnetic declination.
- Part 4
Distance on Earth: Flat Map, Sphere or Ellipsoid?
Compare local flat distance, spherical great-circle distance and ellipsoid-aware thinking.
- Part 5
Dead Reckoning: Navigating with Speed and Direction
Show how position can be propagated from speed, heading and time, and why error accumulates.
- Part 6
Measurement Noise: Why One Reading Is Not Enough
Introduce noise, bias, precision, accuracy and uncertainty ellipses.
- Part 7
Combining Measurements: The Simplest Sensor Fusion Demo
Derive weighted averaging as a first step toward Kalman filtering.
- Part 8
From Guessing to Filtering: Prediction Plus Correction
Introduce recursive filtering using prediction and measurement update.
- Part 9
How GPS/GNSS Positioning Works Without Equations First
An intuitive explanation of satellite ranging, pseudoranges, trilateration, and clock bias in GNSS.
- Part 10
Pseudorange: The Distance That Is Not Quite a Distance
Explain pseudorange, clock bias, and why GNSS solves position plus time.
- Part 11
Satellite Geometry and DOP
Show why satellite layout affects position uncertainty in GNSS.
- Part 12
GNSS Error Sources: Atmosphere, Blockage and Multipath
Explain real-world GNSS degradation including atmosphere, blockage, multipath and interference.
- Part 13
Carrier Phase, RTK and Why Centimetres Are Possible
Explain code pseudorange vs carrier phase, integer ambiguity and RTK.
- Part 14
Working with Real GNSS Data: RINEX, Observations and Orbits
Introduce observation data, navigation data, RINEX concepts and simple visualisation.
- Part 15
What an IMU Really Measures
Explain accelerometers, gyroscopes, specific force and why a stationary accelerometer reads gravity.
- Part 16
Strapdown INS: Turning IMU Data into Position
Explain the strapdown chain: gyro integration, attitude, gravity compensation, velocity and position integration.
- Part 17
Why Inertial Navigation Drifts
Show how accelerometer bias, gyro bias and noise grow into large position errors.
- Part 18
IMU Calibration: Bias, Scale and Misalignment
Explain accelerometer and gyro calibration using bias, scale factor and misalignment models.
- Part 19
Attitude: Euler Angles, Rotation Matrices and Quaternions
Explain attitude representations and why quaternions are useful.
- Part 20
Kalman Filter Intuition for Navigation
Explain Kalman gain, covariance and GNSS/INS prediction-correction intuition.
- Part 21
Loose Coupling vs Tight Coupling
Compare fusing a receiver PVT solution against raw GNSS measurements in GNSS/INS integration.
- Part 22
GPS Outages: Tunnels, Cities and Jamming
Explain what happens when GNSS disappears or degrades and how INS and motion constraints help bridge outages.
- Part 23
Practical Land-Vehicle Navigation
Explain why land vehicles can exploit wheels, roads and motion constraints.
- Part 24
Gravity and Navigation: Is Gravity Just 9.81?
Explain normal gravity, the geoid, gravity anomalies, and why gravity matters for INS.
- Part 25
Map Matching and Feature Matching
Explain using roads, gravity, magnetic fields and landmarks as navigation information.
- Part 26
Building a Browser-Based Navigation Lab
Use browser geolocation and device motion APIs safely for reader experiments.
- Part 27
Capstone: Build a Simple GNSS/INS Fusion Simulator
Combine trajectory generation, IMU simulation, GNSS simulation, drift and Kalman fusion into one final interactive tool.