How to quantify dependence between datasets with 2 variables?

[poster]

My final goal is to estimate the 2D position of a target (blue signal on the image) knowing the 2D position of a surrogate. For now, I have two possible surrogates (red and yellow signals) and, before building models, I want first evaluate which one presents the most dependance with the target's signal. I'd like to quantify the strength of the relationship, or in other words, evaluate which surrogate give me the more information about the target.

I've mostly heard about mutual information, correlation and similarity.

For similarity, I could normalize each dataset and rotate them using PCA to finally compare them using some distance metrics, but it seems no really answer to the problem, as there are signals from different objects. Also, it's sensitive to lags or phase differences, which are present in my data.

I tried multiple correlation which is a measure of how well a variable (x or y of my object) can be predicted from a set of other variables (x and y of the surrogate) but it implies only linear relationships. The comparison won't be fair if a surrogate has a strong non-linear relationship with the object while the other has a weaker but linear relationship.

Multivariate mutual information seems to be, by definition, what I'm looking for, but it requires information about the distributions. I've read it's possible to estimate them using counts in bins, but I'm afraid I have not enough data and also it depends on the choice of the bin size.

Would you know another metrics? Maybe in the frequency domain? It must use both x and y positions.

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