In this paper, a data-driven extension of the variational algorithm is proposed. Based on a few selected sensors, target tracking is performed distributively without any information about the observation model. Tracking under such conditions is possible if one exploits the information collected from extra inter-sensor RSSI measurements. The target tracking problem is formulated as a kernel matrix completion problem. A probabilistic kernel regression is then proposed that yields a Gaussian likelihood function. The likelihood is used to derive an efficient and accelerated version of the variational filter without resorting to Monte Carlo integration. The proposed data-driven algorithm is, by construction, robust to observation model deviations and adapted to non-stationary environments.