Local Strong Convexity of Source Localization and Error Bound for Target Tracking under Time-of-Arrival Measurements

In this paper, we consider a time-varying optimization approach to the problem of tracking moving target using noisy time-of-arrival (TOA) measurements. Specifically, formulate as that sequential TOA-based source localization and apply online gradient descent (OGD) it generate position estimates target. To analyze performance OGD, first revisit classic least-squares formulation (static) elucidate its estimation geometric properties. particular, under standard assumptions on TOA measurement model, establish bound distance between an optimal solution true position. Using bound, show loss function in formulation, albeit non-convex general, is locally strongly convex at global minima. best our knowledge, these results are new can be independent interest. By combining them with existing techniques from optimization, then non-trivial cumulative error OGD. Our numerical corroborate theoretical findings OGD effectively track different noise levels.