I am trying to find a method to calculate how far a point lies from the mean of a 2D Gaussian in terms of standard deviations. I have drawn a diagram to demonstrate my problem.
I know the position of the mean, the position of the point and the 2x2 Covariance matrix of the Gaussian.
I am currently using the Gaussian Distribution function to determine the (z-axis) height of the Gaussian curve at the given point, but a standard deviation measurement in the x/y plane is far more valuable to me.
What you are looking for is precisely the Mahalanobis distance of an observation.