Environmental monitoring systems, methods and media

A system for monitoring a physical environmental property having non-stationary heteroscedastic noise is disclosed. A processor receives physical environmental measurement data, and constructs a combined input and output noise levels matrix containing output noise terms associated with the physical environmental property and input noise terms associated with the at least one independent variable. Using the combined input and output noise levels matrix, the processor constructs a main Gaussian Processes (GP) model for the physical environmental property and its non-stationary heteroscedastic noise. The processor generates and co-operates with the output device to perceptibly output a predictive probabilistic representation of the environmental property, using the main GP model. The predictive probabilistic representation includes a respective range of possible values of the physical environmental property for each respective value of the independent variable(s), the range reflecting both the input noise terms and the output noise terms.