In this paper, we analyze DSPSA: a new distributed optimization algorithm for problems involving uncertainties. DSPSA combines Simultaneous perturbation stochastic approximation with consensus protocol and possesses properties of both algorithms. We study this method in the context of parameter estimation problems over large-scale sensor networks. Optimization in such networks may lead to communication overhead. This problem sets new requirements on optimization algorithms that must account for the efficacy of communication. Despite the presence of uncertainties: noise, external disturbance, and time-varying topology due to communication constraints, DSPSA converges to parameters to be estimated. The theoretical results provide an asymptotically efficient upper bound for the residuals. We also ananyze the convergence of the algorithm with the involvmenet of the heavy-ball momemnum term.