From where the Call Stack window information is read?

Dear Keil MDK-ARM uVision support,

I'm using Keil MDK-ARM uVision 5.14 for ARM Cortex-M3 core, STM32F103 device.

From time to time we get a HardFault exception.
We know that if the debugger is connected, it is somehow posible to deduce the offending
instruction/routine by opening the Call Stack window and following the hints. That´s fine.

But what about if you get a HardFault and the debugger is not connected?
When we get the HardFault, we want somehow to read the same information you are reading
for showing the Call Stack window.
Our intention is to read the same information you do and send it to a UART port
to be able to read it with a Hyperterminal or similar.

We know that reading the stack content is the first step. We are doing it already, but
it is not enought for us since in our case the application code is quite complex, and unrolling
the stack contents might be complex.

Thanks a lot for your help.