Read
Read the derivation
The full chapter walks from two ultrasonic ranges to an x/y position, then derives polar components and velocity.
Step 3 · Core path
Radar math from two echo times.
Connect vector math to live sensor data: range, trilateration, bearing, velocity, prediction, and the error budget created by a short sensor baseline.
Practice
- Convert echo time to range using speed of sound.
- Given two ranges and a sensor baseline, solve x/y position.
- Use two positions and dt to compute velocity components.
Calculator backlog
- Echo time to distance.
- Two-circle trilateration.
- Bearing and closing-rate estimator.
- Baseline sensitivity and jitter estimate.
Try it live
The live radar tool runs the same pipeline against streamed data — watch range, bearing, and velocity update in real time.
Open live radarYou're ready to move on when…
- You can turn an echo time into a range and two ranges into an x/y fix.
- You can derive bearing and velocity from two positions and a dt.
- You can explain why a short sensor baseline inflates the error budget.
End of the core path
That completes the core path. Take the radar build end-to-end, or branch into control theory when a project needs a feedback loop.
Open radar project