UWB robot localization

2D range model. Anchor positions are known exactly. The tag and anchors share one elevation; distances are planar. Each measurement has independent zero-mean Gaussian noise. A constant positive bias can be applied to anchor A3 throughout the run.

Estimator. Nonlinear least squares (NLS) fits range residuals using a damped iterative solver initialized by linearized ranging equations. The estimator receives only the measured ranges and anchor coordinates. It uses no true positions, NLOS correction, temporal filtering, or map constraints. Finite estimates can lie outside the room.

Experiment. A prescribed polyline is sampled every 0.1 s at 0.6 m/s, with instantaneous heading changes at corners. The random seed fixes the noise sequence; replay changes only its display. Changing a model parameter recomputes and restarts the run. The 95th percentile uses the nearest-rank convention. Statistics include valid samples only; failed samples are reported separately. Negative simulated ranges invalidate that sample rather than being silently clipped.

Animation. The robot symbol follows the continuous reference position; the blue marker and range values update at 10 Hz. The chassis, turning orientation, wheel treads and radio pulses are schematic. Robot heading comes from the prescribed route, not from UWB localization. Radio pulses do not represent propagation time or a confidence region. Playback speed changes viewing speed only; the physical trajectory remains 0.6 m/s. Scientific exports omit these decorative elements.

Scope. This is an illustrative simulation, not measured UWB performance. Constant bias is a simplified NLOS model. It omits multipath dynamics, packet loss, anchor uncertainty, antenna delays, vertical offsets, and robot dynamics. A physical installation with different antenna heights needs a height-aware range model.

Residual = fitted geometric distance − measured range. The biased anchor, when enabled, is marked with an asterisk.