Unraveling AirTags and UWB – Part 1: Blink Signals and Hyperbolas

Apple’s AirTags feel like magic. Lose your keys, and your phone can guide you to their exact spot. This incredible precision isn't magic—it's a technology called Ultra-Wideband (UWB). But what if we could take that same power and apply it to tracking tools on a factory floor, valuable assets in a warehouse, or vehicles in a large lot?

That's exactly what we're going to explore. In this series, we'll deconstruct how this technology works. For this first part, we will focus on one popular method—Time Difference of Arrival (TDOA)—to locate a tag on a simple 2D plane. Let's dive in.

The "Blink": A Super-Fast Lighthouse

At the heart of UWB is the "blink"—a very short and precise radio pulse sent out by the tag. Think of it like a tiny lighthouse sending out a flash of light. This blink is what makes UWB far more accurate than Bluetooth or Wi-Fi, whose signals are longer and less precise.

The tag we want to find continuously sends out these blinks. The interactive scene below shows a tag blinking, sending its signal outward in all directions.

The "Listeners": UWB Anchors

To "see" these blinks, we need listeners. In an industrial setup, we use devices called UWB anchors. These are placed at fixed, known locations around the tracking area. My TagTrack project involved building custom anchors just like the one on the image below. Their one job is to listen for blinks and record the exact time each one arrives.

From Time Difference to a Curve

Here's where it gets clever. If a tag blinks, and two anchors hear it, the anchor closer to the tag will hear it first. The system measures this tiny difference in arrival time—the Time Difference of Arrival (TDOA).

This time difference doesn't point to a single location. Instead, it defines a curve of all possible locations where the tag could be. This curve is a hyperbola.

In the simulation below, you can get an intuition on how a hyperbola is formed and how it changes depending on the TDOA.

Let`s dive deeper. Move the Tag and notice how:
1. The signal propagates and reaches the two anchors in differtent time.
2. The hyperbola changes shape depending on the time difference of arrival (TDOA) between the two anchors
3. The hyperbola path always passes through the X and Y coordinates of the tag.

X Marks the Spot: Finding the Intersection

A single hyperbola gives us a line of possibilities, but not an exact position. To pinpoint the location, we need at least one more anchor.

Adding a third anchor allows us to create a second hyperbola (using a different pair of anchors). The two hyperbolas will intersect at exactly one point. That intersection is the precise 2D location of our tag!

What's Next

We've successfully located our tag on a 2D plane using TDOA. We've seen how blinks, anchors, and intersecting hyperbolas work together to achieve amazing precision in finding X and Y coordinates.

Why we have to deal with hyperbolas instead of circles?

The real world isn't flat. How do we find an object's vertial position or Z coordinate?