Smoothing readings

The gas sensor in the hangar hangs right next to the vent. Its pressure readings jump by a few kPa every tick, and the control behind it switches the pump on and off every second. The pressure in the room is perfectly calm – only the measurement is jumpy. The fix: smooth the readings before the control loop sees them.

Moving average#

The simplest way: remember the last N readings and take their average. The values live in a ring buffer in the stack, as in the project “Measurement history”. An index runs in a circle and always overwrites the oldest value:

add i i 1
mod i i N            # 0 to N-1, then 0 again
poke i x             # replace the oldest value
move sum 0
move k 0
adding:
get tmp db k
add sum sum tmp
add k k 1
blt k N adding
div mean sum N

A single outlier now counts for only one N-th. In return the average needs N ticks until a real step has fully arrived, and every slot in the buffer costs stack.

Exponential smoothing#

Without a buffer it works with a single formula:

g = g + a · (x − g)

g is the smoothed value, x the new reading, a a share between 0 and 1. Every tick g moves closer to the reading by that share:

sub d x g
mul d d SHARE        # SHARE = 0.25
add g g d

Three lines, one register for the state – no stack, no loop. With a = 0.25 and a step from 100 to 120 kPa, g shows 105, 108.75, 111.6 … one after another and keeps getting closer to the new value.

The start value matters. If g starts at 0, it creeps up to 100 kPa only slowly after switching on – a control loop thinks the room is nearly empty all that time. So set g to the first reading before the main loop.

Noise versus lag#

Smoothing has a price. The stronger you smooth, the later the chip notices a real change:

A display may well be sluggish. For a control loop a little smoothing is usually enough, the hysteresis does the rest.