Speed from Depth/Pressure sensors
All depth measurements I've been able to read are very accurate (±0.1cm)

That's highly unlikely. It seems that something is quantizing your data at pretty rough interval: maybe 2cm or so plus some extra noise. There are is also a spike at t = 2000 units ?) where the depth jumps from 0.1m to about 0.5m in one sample. Your sample interval is 40 milliseconds. 0.5m in 40ms corresponds to a speed of 12.5 m/s. Can your object really move that fast ?
Overall your data looks quite bad (noisy, quantized &amp; spikey) and not like a real physical object tends to behave.

find out the speed of the body by differentiating the measured depth value

The second curve doesn't look the derivative of the first curve at all. I would expect a massive velocity peak of 12.5 m/s at t = 2000, but your velocity curve just shows a minor blip. Another big peak should be at t= 4000. I have no idea what you did there, but it doesn't appear to be differentiation.

This is a simple calculation of the &quot;velocity&quot; from the depth measurements using Excel. It seems more reasonable than the plot in the question.
Note that the data used was from Web Page Digitizer, so it won't be quite the same as the original.


In the future please label the X and Y axis of your graph with proper units. I have no idea what the unit of your velocity are supposed to be but it's unlikely to be in m/s.