Drift-Aware Gaussian Process Nowcasting of Urban PM2.5 from Sparse Reference Monitors and Low-Cost Sensors

Continuous reference-grade monitoring in Indian cities is sparse. A Tier-2 city such as Bhubaneswar relies on a handful of CPCB-grade analysers and on manual stations that sample twice a week, so an hourly PM2.5 map is in practice an extrapolation from three or four points. Low-cost optical sensors can be deployed at ten times that density, but their readings carry multiplicative gain error, offset, humidity-driven over-reading and slow drift, and the correction fitted at deployment is rarely revisited. This paper treats drift correction and spatial nowcasting as a single estimation problem. Each sensor is modelled as an affine, humidity-dependent transform of the true concentration whose gain and offset follow a random walk; a windowed spatio-temporal Gaussian process (GP) anchored to the reference monitors estimates the field, and a block leave-one-sensor-out posterior at each sensor site supplies the regressor for a per-sensor Kalman update of the affine state. No co-location period is required, and one hourly update for 28 sites takes about 31 ms on a single core. In a 40-day winter simulation parameterised on CPCB and OSPCB statistics (city mean 61 µg m−3, four references, 24 sensors reading 80 % high before correction), the method lowers grid-wide RMSE from 12.7 to 11.3 µg m−3 against a reference-only GP, lowers error at held-out reference sites by 30 %, and brings the error of the corrected sensor readings from 54.9 (raw) to 8.2 µg m−3 against a noise floor of 4.0, while a calibration frozen after one week has degraded to 12.7 by the end of the record. A 25 % fouling step is absorbed within two to four days. The shortfalls are reported with equal weight: uncalibrated sensors are worse than no sensors, dropping the humidity term removes the benefit of the sensors entirely, the 90 % predictive intervals cover only 58 % of truth, and a perfectly calibrated oracle shows that most of the remaining error is a representativeness floor set by sensor density rather than by calibration.