We investigate the problem of cooperative self-navigation (CSN) for multiple mobile sensors in the mixed line-of-sight (LOS) and non-line-of-sight (NLOS) environment based on measuring time-of-arrival (TOA) from the cooperative sensing. We first derive an optimized recursive Bayesian solution by adopting a multiple model sampling based importance resampling particle filter for the development of CSN. It can accommodate non-linear signal model and non-Gaussian position movement under different levels of channel knowledge. We also utilize a Rao-Blackwellisation particle filter to split the original problem by tracking the channel condition with a grid-based filter and estimating the position with a particle filter. The CSN with position and channel tracking exhibits advantage over the noncooperative methods by utilizing additional cooperative measurements. It also shows improvement over the methods without channel tracking. Simulation results validate that both schemes can take the advantage of cooperative sensing and channel condition tracking in mixed LOS/NLOS environments, which motivates future research of cooperative gain for navigation and localization in a more general environment.