Passive localization and synchronization in the presence of affine clocks

We consider the passive localization problem in a wireless network, where source nodes at unknown positions are emitting arbitrary signals at unknown time. The receiving asynchronous anchor nodes act passively as they do not cooperate with the source nodes. In order to localize the source nodes, the local receive times from the anchors are collected at a central processing unit. As the estimation of the location also involves the unknown clock parameters and the send times as variables, it is difficult to directly compute a maximum a-posterior estimate. Here, we derive a low-complex iterative solution based on the expectation-maximization algorithm. In contrast to previous works, we consider asynchronity in clock offset and skew by using an affine clock model. By numerical analysis we demonstrate that the proposed scheme performs close to the CRLB and is applicable to scenarios, where the employment field of source nodes is bounded by anchor nodes.