This paper addresses the challenge of achieving robust and reliable positioning of a radio device carried by an agent, in scenarios where direct line-of-sight (LOS) radio links are obstructed by the agent. We propose a Bayesian estimation algorithm that integrates active measurements between the radio device and anchors with passive measurements in-between anchors reflecting off the agent. A geometry-based scattering measurement model is introduced for multi-sensor structures, and multiple object-related measurements are incorporated to formulate an extended object probabilistic data association (PDA) algorithm, where the agent that blocks, scatters and attenuates radio signals is modeled as an extended object (EO). The proposed approach significantly improves the accuracy during and after obstructed LOS conditions, outperforming the conventional PDA (which is based on the point-target-assumption) and methods relying solely on active measurements.