Propagation of an Unmodeled Additive Constant in Range Sensor Observations

Abstract

The rangefinder offset, additive constant or zero error is the most basic systematic error affecting the accuracy range measurements. Recent investigations of different systems that feature range measurement have shown that minimally constrained self-calibration adjustments of observations corrupted by an unmodeled rangefinder offset yield near-linear patterns in the range-observation residuals. This paper explains the underlying mathematical cause of this phenomenon for the purpose of assisting systematic error model identification. As a result of the mathematical derivations a new improved (in terms of parameter correlation) method for estimating the rangefinder offset from the sum of residuals of a least-squares adjustment of biased range observations has been developed. The new method is successfully demonstrated on data collected with total stations and ultrawide band ranging radios over two one-dimensional baselines.