In a pulse-position modulation-based ultra-wideband (UWB) communication system, multiple access is enabled by assigning unique time-hopping sequences to different users. Each user's data information is carried by positions of short pulses which are directly transmitted through an unknown and possibly dense multipath channel. Single-user channel estimation methods have been proposed by maximum likelihood optimization that treats multiple access interference as Gaussian noise. In this paper, multiuser channel estimation methods are proposed based on a pulse-rate discrete-time system model and up to the second-order statistics of the channel outputs. The model can be regarded in a trilinear structure and also resembles a code-division multiple-access (CDMA) system with newly defined hopping-code dependent matrices and inputs for each user. Considering that either the mean or covariance of received signals contains sufficient information for all unknown channels, least squares and covariance matching ideas are successfully applied to estimate all channels blindly. Accordingly, closed-form solutions are derived. Those channel estimates can be used to design typical linear receivers. Performance of each proposed estimator is analyzed and also verified by computer simulations. Corresponding receivers' performance is also studied numerically.