Demo — Geolocation Explorer#
One bearing is a line; cross two and you have a fix. But the quality of that fix is set almost entirely by geometry — the angle at which the bearings cross — not by how good the receivers are. This demo lets you drag the receivers and the emitter and watch the error ellipse breathe.
The idea#
Each receiver gives a line of position with an angular uncertainty band. The fix lives where the bands overlap, and the shape of that overlap is governed by the cut angle: near \(90^\circ\) gives a tight, near-circular error; a shallow cut smears it along range.
Interactive demo#
Walkthrough#
Start with a good cut. With the emitter abeam the receiver pair, the two bearings cross near \(90^\circ\) and the error ellipse is small and round. Note the CEP readout.
Push the emitter downrange. As it moves far from the baseline, the cut angle shrinks, the ellipse stretches along the line of sight, and CEP grows — the same receivers now do far worse.
Drag onto the seam. Move the emitter onto the receivers’ baseline. The cut collapses, range becomes unobservable, and the fix runs away — the geometry has failed, not the hardware.
Widen the baseline. Drag one receiver out perpendicular to the line of sight to reopen the cut toward \(90^\circ\) and watch the ellipse tighten again.
Key observations#
Geometry sets the error, not receiver quality. This is the whole lesson — the receivers never change in the type-along; only the geometry does.
A shallow cut smears error along range. Cross-range stays decent; downrange blows up.
Wide baselines hold a strong cut at long range — exactly the standoff geometry Project 2 exploits to geolocate from outside the threat rings.
Source#
MATLAB · code/L14_TwoReceiverCrossFix.m↓
The in-class script crosses two noisy bearings into a fix, repeats it thousands of times to map the error cloud, then moves the emitter downrange to show the same receivers degrade as the cut angle shrinks.