Environmental monitoring systems, methods and media

A system for monitoring a physical environmental property that has non-stationary heteroscedastic noise, the system comprising:

• a database defined in a storage medium and configured to receive and store physical environmental measurement data comprising measured values of:
• a dependent variable which represents the physical environmental property;
• and
• at least one independent variable with which the physical environmental property is correlated;
• a processor in communication with the storage medium;
• a communications interface in communication with the processor;
• an output device in communication with the processor;
• and
• a computer-readable medium in communication with the processor;
• wherein the computer-readable medium stores executable instructions that configure the processor to execute a method comprising:
• the processor receiving the physical environmental measurement data;
• the processor constructing 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 with which the physical environmental property is correlated;
• using the combined input and output noise levels matrix, the processor constructing a main Gaussian Processes (GP) model that models the physical environmental property and its non-stationary heteroscedastic noise;
• and
• the processor generating and co-operating with the output device to perceptibly output a predictive probabilistic representation of the environmental property, using the main GP model, wherein the predictive probabilistic representation comprises a respective range of possible values of the physical environmental property for each respective value of the at least one independent variable, the range of possible values reflecting both the input noise terms associated with the independent variable and the output noise terms associated with the physical environmental property.

An environmental monitoring system comprising:

• a storage medium comprising a database storing physical environmental data comprising values of:
• at least one independent variable;
• and
• a dependent variable representing a dependent observed physical environmental property that is correlated with the independent variable;
• a processor in communication with the storage medium;
• a communications interface in communication with the processor;
• an output device in communication with the processor;
• and
• a computer-readable medium in communication with the processor;
• wherein the computer-readable medium stores executable instructions that configure the processor to:
• use a composite covariance function to generate an environmentally adapted covariance matrix corresponding to the values of the at least one independent variable, the composite covariance function comprising at least one stationary term comprising a rational quadratic term, and at least one non-stationary term;
• receive a new value of the at least one independent variable through the communications interface;
• and
• use the environmentally adapted covariance matrix and the physical environmental data to generate a predictive probabilistic representation of a range of possible values of the dependent observed physical environmental property corresponding to the new value of the at least one independent variable, the predictive probabilistic representation having moments including an expected value of the dependent variable and a variance;
• and
• cause the output device to perceptibly output the predictive probabilistic representation.