Observability Analysis of Simultaneous Localization & Calibration for Cooperative Radio Navigation

Kurzfassung

Future robotic surface exploration missions, e.g. on Mars, demand robust and accurate navigation solutions. Since no Satellite Navigation or infrastructure exists on Mars, accurate navigation remains challenging. Cooperative radio navigation emerged as a key technology in such scenarios. Methods based on signal propagation time, such as round-trip time ranging, require sub-nanosecond Time-of-Flight measurement accuracy. However, environmental factors, e.g. temperature changes, can affect group delays of radio transceivers, introducing ranging bias. Simultaneous Localization and Calibration (SLAC) has been proposed to jointly estimate node positions and ranging bias as a calibration parameter, correcting such biases online. However, the success of this calibration process relies on the observability of the calibration and localization parameters, ensuring they can be accurately estimated and corrected using available measurements. To cope with that, we conduct an observability analysis of SLAC, leveraging the equivalence between the full column rank of the Fisher Information Matrix and the measurement Jacobian matrix. This analysis leads to the derivation of necessary and sufficient conditions for observability, which determine the minimum number of static and mobile nodes required for SLAC, and identifies geometric configurations that result in strong, weak, or non-observable systems. We further highlight scenarios where observability is inherently impossible and propose practical solutions for both cooperative and non-cooperative navigation. The analysis is validated through extensive simulations and real-world experiments using radio nodes integrated into static and mobile platforms. The experiments confirm the theoretical findings and demonstrate that SLAC can achieve observability under realistic deployment conditions