Simultaneous perturbation stochastic approximation (SPSA) algorithm is also often referred as a Kiefer-Wolfowitz algorithm with randomized differences. Algorithms of this type are widely applied in field of intelligent control for optimization purposes, especially in a high-dimensional and noisy setting. In such problems it is often important to track the drifting minimum point, adapting to changing environment. In this paper application of the fixed gain SPSA to the minimum tracking problem for the non-constrained optimization is considered. The upper bound of mean square estimation error is determined in case of once differentiable functional and almost arbitrary noises. Numerical simulation of the estimates stabilization for the multidimensional optimization with non-random noise is provided.