Influence of Transmitter Arrangement on Localization Accuracy in Radio–Ultrasonic RTLS in Underground Roadways

This paper presents a sensitivity analysis of positioning accuracy in a localization system based on signal time-of-flight measurements, intended for operation in underground roadway workings. The underground environment is characterized by limited installation space, numerous obstacles causing multipath propagation, and the presence of sections with non-uniform geometry, which in practice leads to a “flattening” of the transmitter constellation and a deterioration of the conditioning of the trilateration problem. As a result, even small changes in input parameters (e.g., related to infrastructure geometry, distance-measurement quality, or the adopted model) may cause a significant change in the position-estimation error, thereby reducing the reliability of roadheader localization across the entire working area. In this study, a local sensitivity analysis is employed to identify the parameters that dominate the positioning outcome. Sensitivity coefficients are defined in a normalized form and are determined numerically using a perturbation approach (changing a given input parameter by a prescribed percentage), which avoids analytical differentiation of the complex relationships arising from the trilateration equations. The analysis is performed for a roadway scenario supported by an ŁP10 steel arch yielding support, with transmitters installed under the support arch and the roadheader trajectory represented by a sequence of consecutive position vectors. The obtained results allow the solution’s susceptibility to errors and uncertainties in the parameters to be assessed and indicate which parameters require priority control in practical implementation. On this basis, recommendations are formulated for the design and maintenance of the localization infrastructure, including transmitter placement and reconfiguration rules (relocation or adding an additional transmitter), to maintain stable positioning quality under operational mining conditions.