The objective of source seeking problems is to determine the minimum of an unknown signal field, which represents a physical quantity of interest, such as heat, chemical concentration, or sound. This paper proposes a strategy for source seeking in a noisy signal field using a mobile robot and based on a stochastic gradient descent algorithm. Our scheme does not require a prior map of the environment or a model of the signal field and is simple enough to be implemented on platforms with limited computational power. We discuss the asymptotic convergence guarantees of algorithm and give specific guidelines for its application to mobile robots in unknown indoor environments with obstacles. Both simulations and real-world experiments were carried out to evaluate the performance of our approach. The results suggest that the algorithm has good finite time performance in complex environments.