Model confidence or uncertainty is critical in autonomous systems as they directly tie to the safety and trustworthiness of
the system. The quantification of uncertainty in the output decisions of deep neural networks (DNNs) is a challenging
problem. The Bayesian framework enables the estimation of the predictive uncertainty by introducing probability distributions
over the (unknown) network weights; however, the propagation of these high-dimensional distributions through
multiple layers and non-linear transformations is mathematically intractable. In this work, we propose an extended variational
inference (eVI) framework for convolutional neural network (CNN) based on tensor Normal distributions (TNDs)
defined over convolutional kernels. Our proposed eVI framework propagates the first two moments (mean and covariance)
of these TNDs through all layers of the CNN. We employ first-order Taylor series linearization to approximate the mean
and covariances passing through the non-linear activations. The uncertainty in the output decision is given by the propagated
covariance of the predictive distribution. Furthermore, we show, through extensive simulations on the MNIST and
CIFAR-10 datasets, that the CNN becomes more robust to Gaussian noise and adversarial attacks.