Anomaly score calculation for multidimensional data set
One very simple yet efficient way, is auto-regression, which means, you train a regressor on past data, and predict the future, if the prediction is off by too much - then you call it an anomaly.

to make it more formal, if we denote $\vec{v}_{t0}$  as your data at timestamp $t_0$, we train a regression model $R$ that learns from $\{v_{t_0},\dots,v_{t_{n-1}}\}$.

Your anomaly score is a function of $R({v_{t_0},\dots,v_{t_{n-1}}})-v_{t_n}$