Mixtures of Gaussian processes for robotic environmental monitoring of emission sources

Emission of greenhouse gases such as methane and carbon dioxide is a known driver of atmospheric heating. Traditional and emerging industries need innovative solutions to comply with increasingly strict sustainability demands and document environmental impact. Mobile sensor platforms such as aerial or underwater vehicles with a high degree of autonomy present a cost-efficient option for environmental monitoring. Autonomous vehicles commonly use Gaussian processes (GPs) for online statistical modelling of concentrations of environmental features. Emission sources in the monitoring area introduce a complication, since the variance is likely heterogeneous between areas dominated by influx and areas with background concentrations. Mixtures of GPs have previously been demonstrated to be effective in such scenarios. Mixture methods distinguish between the natural background concentration and emission to improve model performance when predicting concentrations and variance at unsampled locations. The mixing of GP models allows for nonstationarity and anisotropy in the modelled spatial dynamics, which is desirable for emission modelling in environments with advective forces such as wind or water current. In this paper, we compare different approaches to spatial concentration modelling that accommodate heterogeneous dynamics, based on mixtures of GPs. Distinction of background and emission is either data-driven or derived from domain knowledge. The predictive performance of different mixture methods is demonstrated on field measurements near emissions and compared in an online path planning context. We identify and discuss important trade-offs between data-driven and knowledge-based clustering of measurements. Results show that mixture methods give realistic variance estimates, suitable for online planning.