Autocorrelation Function Kalman Filter (ACF-KF) Design for Adaptive Measurement Scheduling in Multi-Channel LoRaWAN Sensor Networks

Abstract

Frequent acquisition and wireless transmission can dominate the energy budget of autonomous wireless environmental sensing systems (including water quality monitoring), particularly when measurements activate pumps and high-power optical hardware. This paper presents an autocorrelation-aware Kalman filter (ACF–KF) for multichannel prediction and adaptive measurement scheduling. The method is evaluated using 458 records acquired at 15-min intervals during a nominal five-day deployment. Seven channels are analyzed: temperature, battery voltage, turbidity, low- and high-sensitivity phycocyanin (PC), and low- and high-sensitivity chlorophyll-a (CHL). After excluding the initial transient from model identification, 96 samples form a 24-h learning set and 361 samples are held out for evaluation. Each channel is modeled with a local-linear KF. Lag-one autocorrelation of recent innovations is used to adapt the process-noise covariance when persistent correlation indicates under-modeled dynamics. Relative to a fixed-covariance KF, ACF–KF reduces held-out one-step RMSE by 1.9–6.7% and MAE by 2.9–8.5% across all channels, while reducing pooled median recovery time for learning-defined upper-quintile changes from 45 to 30 min. A scheduler using a temperature sentinel, predicted uncertainty, predicted state change, and a maximum gap constraint reduces full sensing cycles by 52.6%, increasing the mean full-cycle interval from 15 to 31.7 min with 5.83% mean reconstruction NRMSE. Fixed-interval analysis from 15 to 240 min further quantifies the sampling–accuracy tradeoff.