RangeUncertainties

Range uncertainties describe the lack of perfect knowledge of the distance from a sensing device to a target. If r_true is the true range and r_meas is the measured range, then r_meas = r_true + e, where e is the error term that may include a systematic bias and a random component.

Sources of range uncertainty include instrument bias due to calibration errors, timing jitter, and incomplete sampling; environmental effects such as air or water properties, temperature, humidity, and refractive index; propagation path variations and multipath reflections; motion of the platform; and data processing or synchronization inaccuracies. The magnitude and character of these errors can depend on range, environment, and sensor design.

Characterizing uncertainty involves an error model and statistics such as standard deviation or RMSE. In many systems e is approximated as Gaussian with possible nonzero bias and range-dependent variance. Sensor fusion and state estimation methods, including Kalman filtering and Bayesian inference, can combine measurements to reduce overall uncertainty.

Reduction strategies include thorough calibration, higher measurement bandwidth, environmental compensation, motion stabilization, averaging or multi-shot techniques, and using auxiliary sensors to constrain the range. Proper error budgeting and simulation (e.g., Monte Carlo) help predict performance under varying conditions and guide design choices.

Range uncertainty is a critical consideration in surveying, autonomous navigation, robotics, lidar and radar remote sensing, underwater acoustics, and astronomy, where accurate distance estimates impact mapping, localization, and mission reliability.