Mahalanobis Distance

stateEstimation Measures the “distance” a point is from a distribution. It measures the number of standard deviations a point is from a distribution.

In component form:

$$D_M^2=\sum _{i=1}^p\sum _{j=1}^p(x_i-{\mu }_i){\Sigma }_{ij}^{-1}(x_j-{\mu }_j)$$

In matrix form:

$$D_M^2(\mathbf{x})=(\mathbf{x}-\mathbf{\mu }{)}^T{\Sigma }^{-1}(\mathbf{x}-\mathbf{\mu })$$

Note, this looks like the inside of the exponential of a Multivariate Gaussian! And it is!

$D_M^2$ measures the number of standard deviations a point is from the distribution.

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