Strapdown INS: Turning IMU Data into Position

A strapdown INS keeps the IMU fixed to the vehicle body and uses computation to transform body-frame measurements into a navigation frame. Groves’ tutorial covers strapdown inertial navigation, attitude determination, integration and alignment.¹ Woodman’s report gives an accessible introduction to strapdown inertial navigation using MEMS sensors and discusses drift.²

The problem

An IMU measures angular rates and specific force in the sensor/body frame. A navigation solution needs attitude, velocity and position in a navigation frame. The strapdown algorithm is the chain connecting those ideas.

The model

A simplified strapdown loop is:

1. Integrate gyro rates to update attitude.
2. Rotate measured specific force into the navigation frame.
3. Add gravity back to recover acceleration.
4. Integrate acceleration to velocity.
5. Integrate velocity to position.

Gyro update, conceptually:

$$\dot{\mathbf{q}} = \frac{1}{2}\mathbf{q}\otimes \begin{bmatrix} 0 \\ \boldsymbol{\omega} \end{bmatrix}$$

Specific force to acceleration:

$$\mathbf{a}_n = \mathbf{C}_{b}^{n}\mathbf{f}_b + \mathbf{g}_n$$

Velocity update:

$$\mathbf{v}_{k+1}=\mathbf{v}_{k}+\mathbf{a}_{n,k}\Delta t$$

Position update:

$$\mathbf{p}_{k+1}=\mathbf{p}_{k}+\mathbf{v}_{k}\Delta t+\frac{1}{2}\mathbf{a}_{n,k}\Delta t^2$$

This is a teaching simplification. A full mechanisation includes Earth rotation, transport rate, detailed gravity and frame choices.

Interactive demo: strapdown INS simulator

The simulator below implements that 2D yaw-only loop directly, so you can see each stage of the mechanisation chain feed the next.

What to watch

• With perfect sensors, the estimate follows the truth route closely.
• Accelerometer bias grows into a clear position drift.
• Gyro bias causes heading drift, which rotates acceleration into the wrong direction.
• Removing gravity compensation produces immediately unrealistic behaviour.

Try this

Run the stationary case with zero bias. The position should remain close to the origin. Then add a tiny accelerometer bias and observe quadratic-looking position drift.

Where this breaks

A browser demo should not pretend to be a certified INS. It is a mechanisation teaching tool. Real systems require careful sensor calibration, frame conventions, numerical integration, Earth models, alignment and external aiding.

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. ↩

2. Oliver J. Woodman, “An introduction to inertial navigation”, University of Cambridge Computer Laboratory Technical Report UCAM-CL-TR-696, 2007. https://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-696.html - Accessible report on MEMS strapdown INS error characteristics and drift growth. Accessed 2026-06-11. ↩