How to choose the "best" measurment (from a given set) as input for a kalman filter? Problem: 
For an object tracking scenario with multiple objects and multiple tracks, I want to choose the "best" assignment object&lt;->track. Therefore, I need a parameter indicating how suitable an object is for a track.
(Each object refers to a measurement and each track is a Kalman filter)

Idea: 
Given the classical Kalman filter with the matrices state $x$ and measurement transition $H$
We can calculate the residual $y_t$ between the predicted measurement $x_{pred}$ and the measurement $z$ by:

$y_t = z-H x_{pred}$

However, this will be a vector. Is there a general approach to reduce this to one parameter? (e.g distance when having just position information). I assume that some kind of normalisation is needed to get all the residuals for each state in the same range? Building the l2-norm would be my first approach.

Question: 
Which parameter is suitable to indicate how "good" the measurement fits to the Kalman filter?

Is the residual suitable? If so, how to handle different value ranges, and how to "compress" the vector to just one value?
Question: Which parameter is suitable to indicate how "good" the
  measurement fits to the Kalman filter?


To estimate a quality of association you can use likelihood function. The likelihood considers not only residual but also uncertainty and represented as scalar value:

$$\mathcal{L} = \frac{1}{\sqrt{2\pi S}}\exp [-\frac{1}{2}\mathbf y^\mathsf T\mathbf S^{-1}\mathbf y]$$


  Problem: For an object tracking scenario with multiple objects and
  multiple tracks, I want to choose the "best" assignment
  object&lt;->track.


The question which you are interested is called data association and as was said there are a lot of solution and this question is too broad. Here are some of methods (you can google it and find more information):
 - Global nearest neighbour (in Euclidean space);
 - Global strongest neighbour;
 - Joint probability data association;
 - Multiple hypothesis tracking (the best choice).