In time of arrival (TOA) estimation of received ultra-wideband (UWB) pulses, traditional maximum likelihood (ML) and generalized likelihood estimators become impractical because they require sampling at the Nyquist rate. Sub-Nyquist ML-based TOA estimation currently assumes a priori knowledge of the UWB channels in the form of the average power delay profile (APDP). In this paper, instead of assuming a known APDP, we propose and investigate a joint estimator of the TOA and the APDP. We assume a multi-cluster parametric APDP model and estimate its parameters via a least-squares approach; the estimated APDP is then used in connection with a ML criterion to obtain the TOA estimate. The proposed method has a low sampling rate requirement and is well-suited for real-time implementation. Simulation results show that it can achieve improved accuracy in practical UWB TOA estimation scenarios, when compared to other competing approaches.