Fusing Two Temperature Sensors with a Kalman Filter: A Monte Carlo Simulation of Noise, Drift and an Unmodelled Step

Redundant temperature sensors are common in cyber-physical systems, but the best way to combine them depends on the process that is being measured. This paper simulates a room temperature modelled as a random walk with an added 2 K step, measured by two sensors with noise standard deviations of 0.5 K and 1.5 K, and compares five estimators in 200 Monte Carlo runs. A Kalman filter that fuses both sensors reached a root-mean-square error (RMSE) of 0.094 K before the step, compared with 0.499 K for the better sensor alone and 0.152 K for a 10-sample moving average of the weighted mean. However, because the step was not part of the filter's process model, the Kalman filter needed on average 48 samples to recover after the step versus 10 for the moving average, and its RMSE over the whole record (0.236 K) was higher than that of the moving average (0.187 K). The overall RMSE was lowest when the assumed process-noise variance was about 25 times the true value. The study is a simulation of an idealised scalar process. This is a simulation study; all results are outputs of the deposited Python code with assumed parameters. Source code is attached.