Optimizing the performance of Kalman filter based statistical time-varying air quality models

In this study, the Bayesian approach is proposed to estimate the noise variances of Kalman
filter based statistical models for predicting the daily averaged PM10 concentrations of a typical
coastal city, Macau, with Latitude 22°10’N and Longitude 113°34’E. By using the
measurements in 2001 and 2002, the Bayesian approach is capable to estimate the most
probable values of the noise variances in the Kalman filter based prediction models. It turns
out that the estimated process noise variance of the time-varying autoregressive model with
exogenous inputs, TVAREX, is significantly (~76%) less than that of the time-varying
autoregressive model of order 1, TVAR(1), since the TVAREX model incorporates important
mechanisms which govern the daily averaged PM10 concentrations in Macau. By further using
data between 2003 and 2005, the choice of the noise variances is shown to affect the model
performance, measured by the root-mean-squared error, of the TVAR(p) model and the
TVAREX model. In addition, the optimal estimates of noise variances obtained by Bayesian
approach for both models are located in the region where the model performance is
insensitive to the choice of noise variances. Furthermore, the Bayesian approach will be
demonstrated to provide more reasonable estimates of noise variances compared to the
noise variances found by simply minimizing the root-mean-squared prediction error of the
model. By comparing the optimized TVAREX model and the TVAR(p) models in predicting the
daily averaged PM10 concentrations between 2003 and 2005, it is found that the TVAREX
model outperforms the TVAR(p) models in terms of the general performance and the episode
capturing capability.