Tracking of multiple targets is a classical problem in signal processing that arises in many applications, e.g. air, maritime and road traffic control. Networks of autonomous sensors serve as desirable platforms for multi-target tracking in view of their redundancy and reconfigurability. The networked implementation, however, makes it impossible to use classical centralized approaches to filtering, since each sensor has limited computational capabilities and restricted access to the measurements of other sensors. Besides topological constraints (each sensor can interact only to a few adjacent nodes of a network), communication between sensors can be restricted, due to e.g. limited capacity of communication channels, delays and data distortions.In this paper, we propose a new algorithm for distributed multi-target tracking in a sensor network. The algorithm is based on the seminal idea of simultaneous perturbation stochastic approximation (SPSA), being a special case of stochastic gradient descent algorithm. The important feature of the SPSA method is the ability to solve optimization (in particular, optimal tracking) problems in the presence of arbitrary unknown (but bounded) disturbances and time-varying parameters of the system. These uncertainties need not be random, and even if they are random, one need not know their statistical characteristics. We provide the mathematical results on stabilization of the mean-square estimation error and analyze its dependence on the choice of step-size parameters. Theoretical results are illustrated by numerical simulations.