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Version devBuilt at: 2026-10-10 01:38:52 EDT

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@daniel.colquitt.xyzOct 4, 2026, 2:10 PM

Tap-water nitrate T is modelled separately as a slowly varying Gaussian random walk. That is an assumption, but a more plausible one than treating the supply as perfectly constant.

[4/10]

#Aquarium #KalmanFilter #Fishkeeping #PlantedTank

@daniel.colquitt.xyzOct 4, 2026, 2:09 PM

This is the same mathematics as the “nearly constant velocity” model used in target tracking: N takes the role of position and r of velocity.

[3/10]

#Aquarium #KalmanFilter #Fishkeeping #PlantedTank

@daniel.colquitt.xyzOct 4, 2026, 2:09 PM

My hidden state is

x = (N, r, T)

with r the net accumulation rate and T the nitrate concentration of the tap water.

[2/10]

#Aquarium #KalmanFilter #Fishkeeping #PlantedTank

@daniel.colquitt.xyzOct 4, 2026, 2:08 PM

I have, perhaps inevitably, built a Gaussian assumed-density filter (GADF) to estimate nitrate in my #Aquarium .

I initially thought of it as a #KalmanFilter , but parts of the physical and measurement model are non-Gaussian, so GADF is the more accurate description.

Home Assistant dashboard showing the aquarium nitrate model over 2–4 October 2026. The blue curve is estimated nitrate concentration with a shaded 95% uncertainty interval; the green curve is estimated net nitrate accumulation rate with its 95% interval. The current summary reports nitrate 7.90 ± 1.74 ppm, net accumulation 2.29 ± 1.32 ppm/week, and tap-water nitrate 4.28 ± 1.51 ppm. The filter has only been running for a few days, so the estimates and uncertainty are still settling.
@daniel.colquitt.xyz.ap.brid.gyOct 4, 2026, 2:04 PM

I have, perhaps inevitably, built a Gaussian assumed-density filter (GADF) to estimate nitrate in my #Aquarium.

I initially thought of it as a #KalmanFilter, but parts of the physical and measurement model are non-Gaussian, so GADF is the more accurate […]

[Original post on colquitt.xyz]

Home Assistant dashboard showing the aquarium nitrate model over 2–4 October 2026. The blue curve is estimated nitrate concentration with a shaded 95% uncertainty interval; the green curve is estimated net nitrate accumulation rate with its 95% interval. The current summary reports nitrate 7.90 ± 1.74 ppm, net accumulation 2.29 ± 1.32 ppm/week, and tap-water nitrate 4.28 ± 1.51 ppm. The filter has only been running for a few days, so the estimates and uncertainty are still settling.