Low-cost VIO and the DVL question
When you can’t buy the sensor, you have to earn its measurement from the ones you have. A note on fusing depth, flow and heading honestly.
A right-invariant EKF is the spine of the localization stack: it predicts on the board’s IMU and corrects with everything cheap we can measure — depth, optical-flow velocity, heading, and occasional fixes from recognised props.
The subtle part is time. Measurements arrive late — a detection is a description of where the vehicle was when the shutter opened, not where it is now. Applying it on arrival smears the estimate. So late measurements are replayed at the instant they describe, and the filter’s history is corrected from there forward.
An absent prediction must never be read as a permissive one.
Fusion is where optimism hides. A prior should stop helping exactly when it stops being one; a gate should weaken exactly when the prior stops being worth trusting. Get that backwards and the vehicle steers confidently at nothing.
The DVL question — do we need the expensive sensor? — is not answered by a spec sheet. It is answered by whether the cheap estimate clears the bar the mission needs, measured in water. Until then, the honest state is written down, not assumed.