Marco Polo: Finding a friend with only distance and motion
2 days ago
- #sensor-fusion
- #kalman-filter
- #localization
- The problem involves finding a friend in a crowded cafe using only distance and motion data, analogous to locating devices using sensors without prior infrastructure.
- Inertial measurement units (IMUs) provide acceleration and heading data, while ultra-wideband (UWB) units measure distance via time-of-flight, but lack bearing information.
- Phase difference of arrival (PDoA) UWB can determine bearing using two antennas, but is challenging for wearables due to signal attenuation and design constraints.
- Trilateration with external anchors (like GPS) requires fixed reference points, making it impractical for environments without installed equipment.
- An extended Kalman filter (EKF) is chosen for state estimation, as it supports nonlinear functions, works with a single UWB antenna, and requires only two devices.
- The EKF tracks state variables (x, y distance, velocities) and uses prediction and measurement steps to update estimates, linearizing nonlinear functions via Jacobians.
- State prediction uses physics equations with control inputs from IMU data, while measurement updates incorporate UWB distance readings to refine position estimates.
- The filter initializes with UWB distance and assumes an initial direction along the x-axis, accumulating bearing belief as the device moves.
- The EKF outputs bearing and uncertainty, enabling localization in a 2D plane, demonstrated through an interactive simulation of device movement.
- Kalman filters have broad applications in robotics and navigation, with extensions like unscented Kalman filters offering advanced options for future use.