Finding dependence between two sparse signals
If you have enough sample measurement data, you could reconstruct a time series for each sensor pair that eliminates any time step where either one or both of the sensor pairs are na.  Then you are left with a time series for that pair without any na's and can proceed with standard time series approaches for calculating correlation.  Then repeat those steps for each sensor pair.

For example:

X_1 = [2, 5, 1, na, na, 1, na, na, 89]
X_2 = [na, 4, 9, 8, na, na, na, 2, 9]


after reconstruction becomes:

X_1 = [5, 1, 89]
X_2 = [4, 9, 9]