From Arcs to Motion -
Understanding the Signal Story

Turn Calibration - How the Curves Become Headings

How satellite timing, Doppler shift, and turn dynamics transform arcs into a measurable flight path

Curved paths in satellite-based reconstructions are often treated as visual approximations—smooth arcs connecting uncertain positions.

In this framework, curves are not drawings.
They are measurable results of aircraft motion.

Turn Calibration is the process of translating those curves into:

Defined heading changes
Measurable turn rates
Time-aligned motion behavior

This transforms a visual path into a physics-based reconstruction driven by the signal itself.

Satellite data does not directly show a flight path — it shows signals.

BTO (Burst Timing Offset) measures distance from the satellite
BFO (Burst Frequency Offset) measures motion through Doppler shift
Signal Sequencing converts isolated handshakes into continuous behavior

The Etch-a-Sketch Model transforms these signals into motion — one step at a time.

SIGNAL GEOMETRY FRAMEWORK

Understanding the Signal Geometry Framework

This framework organizes how satellite signal data is used to reconstruct aircraft motion.

Rather than treating each measurement separately, the system combines distance, motion, time, and system behaviorinto a single structured model.

🛰️ What You’re Looking At

Each panel represents a core component of the signal:

Range (BTO) defines how far the aircraft is from the satellite
Doppler (BFO) reveals how the aircraft is moving relative to it
Time sequencing connects each measurement into a continuous timeline
System state reflects how onboard systems influence the signal

Individually, these elements provide partial information.
Together, they form a set of constraints that limit where the aircraft can be and how it is moving.

⚙️ How the System Works

The model does not assume a flight path.

Instead, it builds one by:

Applying distance constraints from timing
Applying motion constraints from Doppler
Aligning both across time
Incorporating system events as physical markers

This process transforms signal behavior into a measurable trajectory.

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From Signals to Motion: The Etch-a-Sketch Reconstruction

From Arcs to Trajectory

Traditional interpretations rely on arcs and isolated measurements.
This method goes further — combining timing, frequency, and sequence into a unified motion model.

Instead of asking “Where could the aircraft be?”
we ask:

“Where must the aircraft go next based on the last signal?”

This forward-only constraint eliminates impossible paths and reveals a consistent trajectory.

Step-Based Signal Reconstructionn

Each satellite handshake is not a path — it is a single data point.
The aircraft’s trajectory is revealed only when these points are connected in sequence.

Using a step-based method:

Each BTO defines a position constraint
Each BFO defines a directional movement
Each timestamp locks the sequence in time

The Etch-a-Sketch approach connects these steps forward only — never backward — producing a continuous, physics-based flight path.