In today’s geopolitical environment, a growing number of actors, including nation states, are engaging in techniques known as GPS spoofing and GPS jamming. GPS spoofing involves transmitting counterfeit signals that mislead receivers into calculating incorrect position or time data. GPS jamming, on the other hand, overwhelms receivers with interference, preventing them from acquiring a reliable signal altogether.
For most of us, losing GPS would be an inconvenience. For aviation, it would be something far more serious. Modern airliners depend on accurate navigation not just for efficiency, but for safety. And while GPS has become a cornerstone of navigation, aircraft are not designed to rely on it alone. Redundancy is essential.
This raises an important question, “How does an aircraft know where it is when GPS is unavailable?”
The answer…
At first glance, the answer seems almost too simple. An aircraft can determine its position by keeping track of every movement it makes from a known starting point. If you always know how fast you are moving and in what direction (velocity), you can work out where you are at any moment.
This idea is not new. In fact, it is rooted in calculus.
More on the mathematics…
From basic physics, we know that acceleration is the rate of change of velocity with respect to time.
We also know that velocity is displacement with respect to time.
As explained in a previous post, differentiation tells us that velocity is the derivative of displacement, and acceleration is the derivative of velocity.
The inverse operation of differentiation is integration. Therefore, if acceleration is known, it can be integrated over time to determine velocity. Similarly, since velocity is the rate of change of displacement, it can be integrated to determine displacement. I will explain integration in more detail in a later post.
The Inertial Reference System
Mathematics alone is not enough. The aircraft must first measure its motion with extreme precision. This is the role of the Inertial Reference System (IRS). By combining displacement with a known initial position, the system can continuously update and determine the position of a body, such as an aircraft.
The IRS is a self-contained system that continuously calculates an aircraft’s:
- Position
- Velocity
- Orientation (pitch, roll, and heading)
Crucially, it does all of this without relying on any external signals.
Before take-off, the system is aligned with a known position. From that moment on, it begins tracking every movement of the aircraft.
Measuring motion in three dimensions
To understand how this works, imagine trying to track motion. You need to measure movement not just forward and backward, but also side-to-side and up-and-down.
Modern IRS units therefore use three accelerometers, each aligned with one of the three axes (x, y, z), to measure acceleration in all directions.
In high-precision aviation systems, these are typically quartz-based accelerometers, designed to detect even the smallest changes in motion.
How acceleration is measured
One common design is the quartz flexure accelerometer.
Inside the device is a small mass, known as a proof mass, suspended on a flexible structure. When the aircraft accelerates, this mass resists the change in motion due to inertia and moves slightly.
This movement is detected as a change in capacitance between nearby surfaces. A feedback circuit then applies a restoring force to push the mass back into its original position.
By measuring the force required to hold the mass in place, the system can determine the applied acceleration with remarkable accuracy.
A different approach: vibrating beams
Another widely used design is the quartz vibrating beam accelerometer.
Here, a small quartz beam is driven at its natural resonant frequency. When acceleration is applied, a proof mass exerts a force on the beam, causing it to stretch or compress slightly.
This changes the beam’s vibration frequency.
Because frequency can be measured with high precision, even tiny changes reveal the applied acceleration.
Knowing which way is “forward”
Measuring acceleration alone is not enough.
To interpret these measurements, the system must also know the aircraft’s orientation i.e. what direction is forward, up, and sideways.
This is where gyroscopes come in.
Modern IRS units use laser-based gyroscopes, such as ring laser or fiber optic gyroscopes. These devices send light in opposite directions around a closed loop. When the aircraft rotates, a tiny difference develops in the path length of the beams (a phenomenon known as the Sagnac effect).
By measuring this difference, the system can determine how the aircraft is rotating in three dimensions.
Putting it all together
With accelerometers measuring motion and gyroscopes tracking orientation, the IRS has everything it needs.
It continuously:
- Measures acceleration
- Determines orientation
- Integrates these values over time
From this, it calculates:
- Velocity
- Position
- Attitude
All without ever needing to look outside the aircraft.
The catch: drift
There is, however, a limitation.
Even the most precise sensors are not perfect. Tiny measurement errors accumulate over time. Because the system continuously integrates these values, small errors gradually grow into larger ones.
This is known as drift. Over long periods, an IRS will slowly lose accuracy.
Why GPS still matters
This is why modern aircraft do not rely on a single system. Instead, they combine:
- Inertial navigation (IRS)
- GPS
- Radio-based navigation
Each system has strengths and weaknesses. By combining them, aircraft achieve both accuracy and resilience.
If GPS is lost or unreliable, the IRS continues to provide a stable, independent reference.
A quiet piece of engineering brilliance
The next time you look at a moving aircraft on a map, it’s easy to assume that satellites are doing all the work.
In reality, deep inside the aircraft, a system is quietly tracking every movement, measuring, calculating, and updating position dozens of times per second.
No signals. No external input. Just physics, mathematics, and some precise engineering.