This paper considers the problem of tracking a timevarying number of non-cooperative emitters based on singlechannel passive sensors, which is traditionally carried out via sequential processing, i.e., detection, measurement extraction and tracking. However, in such a framework, tracking performance is severely affected by the pre-processing steps especially in low signal-to-noise ratio (SNR) scenarios. To remedy this drawback, in this paper we develop an algorithm that directly performs tracking based on the received signals. The states of multiple emitters are represented by a labeled random finite set (LRFS), which is further modeled by a generalized labeled multi-Bernoulli (GLMB) density. A new likelihood model, which inherently exploits time difference of arrival (TDOA) of signals coming from different sensors, is proposed. Then, a new GLMB filter is derived to iteratively compute the posterior of multiple emitters. Moreover, an efficient implementation strategy is devised for the proposed algorithm and its performance is assessed via simulations.