Compensating for measurement errors I have a system where I sample some data periodically (every 10usec). The shape of the data is triangle, in other words it linearly increases and decreases in time. (Both theory and practice are in agreement, I plot the ADC output and I clearly see linear increase and decrease although there is some non-linearity but let's ignore that for the sake of discussion) However the frequency of the signal is not fixed. It may increase very fast or very slow. (narrow or wide triangle)

I am trying to locate the true peak point of the data with 500nsec accuracy, however my ADC samples every 10usec. One item on my favor is that the data values increase and decrease in sequence. I get worst case 50 samples, best case 1000 samples. (in worst case, I will have 25 samples in increasing order and 25 in decreasing order)

How can I approach this issue using DSP techniques? One idea I had was to calculate peak point from rise and fall angles. (I basically extend the left and right side of the triangle and look at where those lines cross each other). I cannot think of any other way. I welcome suggestions.
If you can reliably determine which samples are on a rising portion and which are on a falling portion, then perhaps you can do a linear regression on each (near)monotonic segment, and solve for the intersections of the computed regression lines.

If you know the non-linearity equation, then you can do a regression against that curve instead of using linear regression, and compute or numerically solve for the curve intersections, if needed.

This regression method might also help with error or robustness estimates, if needed.