Braitenberg vehicles have been used for decades to implement source seeking and avoidance behaviours in bioinspired robotics. Recently, new theoretical results have derived convergence conditions of these bio-inspired controllers under the assumption of noiseless sensors. Although Braitenberg vehicles have been experimentally shown to work in outdoor scenarios, there is no theoretical evidence that shows they also can work in perceptually harsh environments. In this paper we mathematically analyse the source seeking behaviour of Braitenberg vehicle 3a with noisy sensors, when noise cannot be ignored. We approximate the stimulus the vehicle is seeking close to a source and derive the evolution equations for the average and covariance of the trajectory realisations. The analysis of the resulting non-linear differential equations shows that, under some conditions, the average trajectory is convergent and the dispersion around this trajectory is bounded. We illustrate these theoretical results through simulations, but also show that our results extend to general source seeking situations where the approximations do not hold.