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Tutorial Series · Part 23 of 27

Practical Land-Vehicle Navigation

Explain why land vehicles can exploit wheels, roads and motion constraints.

By

  • land-vehicle
  • odometry
  • constraints
Series Context

Navigation from First Principles

This article is part of an ordered course. Use the previous and next links to stay in sequence.

Progress Part 23 of 27
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A car is easier to constrain than a drone. It usually travels on a surface, follows roads, has wheel-speed information and rarely moves sideways like a crab. These assumptions can help a navigation filter, especially when GNSS is degraded. Groves’ inertial-sensor tutorial covers motion constraints and related aiding ideas.1

Why vehicles are easier to constrain

An unconstrained INS has to estimate full 3D motion. A road vehicle gives you extra information:

  • Forward speed from wheels or drivetrain.
  • Low vertical velocity most of the time.
  • Limited lateral velocity.
  • Road-network constraints.
  • Frequent stops for zero-velocity updates.

Useful land-vehicle constraints

A non-holonomic constraint for a typical land vehicle says that lateral and vertical body-frame velocities are approximately zero:

vb=[vxvyvz]≈[vx00]\mathbf{v}_b = \begin{bmatrix} v_x \\ v_y \\ v_z \end{bmatrix} \approx \begin{bmatrix} v_x \\ 0 \\ 0 \end{bmatrix}

This can be used as a measurement:

znhc=[00]=[vyvz]+noise\mathbf{z}_{nhc}=\begin{bmatrix}0 \\ 0\end{bmatrix} =\begin{bmatrix}v_y \\ v_z\end{bmatrix}+\mathbf{noise}

Wheel speed gives:

zwheel=vx+noisez_{wheel}=v_x + noise

If the IMU is mounted at an angle, the mounting rotation must be estimated or calibrated:

Cimuvehicle\mathbf{C}_{imu}^{vehicle}

Interactive demo: land-vehicle constraint playground

The interactive view below compares the same route with and without land-vehicle assumptions. It visually damps sideways drift when NHC is enabled, applies stop markers for ZUPT, and shows how mounting error still leaks into the result.

Interactive Demo

Land-Vehicle Constraint Playground

Compare a free-running inertial path against a vehicle-constrained estimate. The map shows drift, the speed trace shows stop events, and the IMU sketch shows how mounting errors weaken the assumptions.

Wheel-speed trace
Vehicle forward axis IMU mounting

Controls

Readouts

Free INS drift0.0 m
Constrained drift0.0 m
Constraint validityvalid
What to noticeNHC suppresses sideways drift when the vehicle assumptions hold.

What to watch

  • Mounting-angle error visibly hurts both heading and position.
  • Non-holonomic constraints reduce sideways wander.
  • ZUPT helps at stops, especially on the stop-start route.
  • Map constraints help keep the estimate road-like, but only if the assumptions are roughly valid.

Try this

Set a 5° yaw mounting error on the square route, then turn off NHC. The path should drift sideways in a way a real car normally would not. Turn NHC and ZUPT back on to see how much those assumptions buy you.

When the assumptions fail

The constraints are not always valid. A vehicle can skid, reverse, go off-road, drive on steep slopes or experience wheel slip. These are useful probabilistic cues, not inviolable truth.

Footnotes

  1. Paul D. Groves, “Navigation Using Inertial Sensors”, IEEE Aerospace and Electronic Systems Magazine, 2015. https://ieee-aess.org/media/navigation-using-inertial-sensors - Tutorial covering inertial sensor technology, strapdown navigation, alignment, zero updates, motion constraints, pedestrian dead reckoning and fault detection. Accessed 2026-06-11. ↩