Theoretical analysis of hybrid RSS and TOA localization with stratified propagation under inaccurate anchors in UAIoTs

Abstract Localization is a crucial technique for determining target locations in underwater acoustic internet of things (UAIoT) systems. However, the presence of stratified oceanic environments and anchor position uncertainties significantly undermine localization accuracy. To rigorously investigate their adverse effects on localization performance, this study presents a comprehensive theoretical analysis of hybrid RSS/TOA-based localization under stratified propagation and inaccurate anchors in UAIoT systems. First, a stratified acoustic propagation model is established, and the corresponding Cram $$\acute{\text e}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mtext>e</mml:mtext> <mml:mo>´</mml:mo> </mml:mover> </mml:math> r-Rao lower bound (CRLB) is derived for RSS and TOA measurements. The analysis is then extended to a hybrid scenario incorporating anchor inaccuracy using the Banachiewicz-Schur theorem, resulting in a unified expression for the theoretical performance bound. Simulation results confirm the validity of the derived CRLB across diverse scenarios. Compared with using a single ranging modality, the derived lower-bound performance of the proposed hybrid RSS/TOA approach improves by at least 19.8% under accurate-anchor conditions and 24.1% under inaccurate-anchor conditions. The findings provide theoretical benchmarks and practical guidance for designing robust localization strategies in stratified oceanic environments.