  Inferring the coupling direction from measured time series of complex systems
is challenging. We propose a new state space based causality measure obtained
from cross-distance vectors for quantifying interaction strength. It is a
model-free noise-robust approach that requires only a few parameters. The
approach is applicable to bivariate time series and is resilient to artefacts
and missing values. The result is two coupling indices that quantify coupling
strength in each direction more accurately than the already established state
space measures. We test the proposed method on different dynamical systems and
analyse numerical stability. As a result, a procedure for optimal parameter
selection is proposed, circumventing the challenge of determining the optimal
embedding parameters. We show it is robust to noise and reliable in shorter
time series. Moreover, we show that it can detect cardiorespiratory interaction
in measured data. A numerically efficient implementation is available at
https://repo.ijs.si/mbresar/cd-vec.
