How do I measure ~16V battery voltage in an ultra low power system?
There are various options, one reasonably simple circuit is this (bias/filter caps and bias voltage circuit not shown for simplicity):



Simulation:

For both graphs the x axis shows the input voltage - top graph is the input voltage itself (not necessary really), and the bottom graph is the output voltage versus the input voltage.
Note that the circuit inverts the signal, so 1.8V = 7V in and 0V = 16V in, but this is easily dealt with in a micro.



The circuit divides by 5 and shifts so the 1.8V span is between 0 and 1.8V. To learn how to calculate and design such circuits, OpAmps for Everyone is a good free book to start with.