In this paper a new distributed time synchronization algorithm is proposed for lossy wireless sensor networks with noisy local clock readings and inter-node communications. The algorithm is derived in the form of two asynchronous recursions of stochastic gradient type providing estimates of the parameters used to compensate drifts and offsets of the local clocks. A special modification of the algorithm for drift compensation based on instrumental variables is introduced in the case of internal measurement noise. It is proved that the proposed algorithm provides asymptotic synchronization in the sense that all the equivalent drifts, as well as all the equivalent offsets, converge in the mean square sense and with probability one to the same random variables.