Uncertainty propagation system and method
The invention provides a method of calculating uncertainty in the system represented as two or more modules comprising the steps of passing uncertainty information from each module to at least one further module; and calculating uncertainty in the measurement result from the information exchanged between the modules. The invention also provides a method of propagating uncertainty in a measurement system and also provides related systems for calculating uncertainty and propagating uncertainty.
1. An uncertainty calculation system represented as a plurality of connected modules:
wherein each module is associated with a set of scalar-valued inputs, one scalar-valued output and one function, in which the function is configured:
to determine the value of the output from the value of each input to the module (module-input), and
to determine for each specific module the contribution to the uncertainty in the value of the output arising from the uncertainty in the value of any input to the system (system-input) as the sum of terms for each module-input;
each term being the partial derivative of the module function with respect to that module-input multiplied by the contribution to the uncertainty in the value of that module-input arising from the uncertainty in the value of that system-input; and
wherein one module has an output that represents a scalar-valued measurement result and in which the contributions to the uncertainty are combined to determine the uncertainty in the measurement result.
2. The system as claimed in claim 1 wherein the system is further configured to calculate the uncertainty in the measurement result as the standard deviation of the statistical distribution associated with the measurement result.
3. An uncertainty calculation system represented as a plurality of connected modules:
wherein each module is associated with a set of vector-valued inputs, one vector-valued output and one function, in which the function is configured:
to determine the value of the output from the value of each input to the module (module-input), and
to determine for each specific module the contribution to the uncertainty in the value of the output arising from the uncertainty in the value of any input to the system (system-input) as the sum of terms for each module-input, each term being the Jacobian matrix of the module function with respect to that module-input multiplied by the contribution to the uncertainty in the value of that module-input arising from the uncertainty in the value of that system-input; and
wherein one module has an output that represents a vector-valued measurement result and in which the contributions to the uncertainty are combined to determine the uncertainty in the measurement result.
4. The system as claimed in claim 3 wherein the system is further configured to calculate the uncertainty in the measurement result as the variance-covariance matrix of the multidimensional statistical distribution associated with the measurement result.
5. A method of calculating uncertainty in the measurement result of a measurement system represented as a plurality of connected modules, the method comprising the steps of:
associating each module with a set of scalar-valued inputs, one scalar-valued output and one function;
using the function to determine the value of the output from the value of each input to the module (module-input);
using the function to determine, for each specific module, the contribution to the uncertainty in the value of the output arising from the uncertainty in the value of any input to the system (system-input) as the sum of terms for each module-input, each term being the partial derivative of the module function with respect to that module-input multiplied by the contribution to the uncertainty in the value of that module-input arising from the uncertainty in the value of that system-input; and
generating an output that represents a scalar-valued measurement result in which the contributions to the uncertainty are combined to determine the uncertainty in the measurement result.
6. The method as claimed in claim 5 further comprising the step of calculating the uncertainty in the measurement result as the standard deviation of the statistical distribution associated with the measurement result.
7. A method of calculating uncertainty in the measurement result of a measurement system represented as a plurality of connected modules, the method comprising the steps of:
associating each module with a set of vector-valued inputs, one vector-valued output and one function;
using the function to determine, for each specific module, the value of the output from the value of each input to the module (module-input);
using the function to determine the contribution to the uncertainty in the value of the output arising from the uncertainty in the value of any input to the system (system-input) as the sum of terms for each module-input; each term being the Jacobian matrix of the module function with respect to that module-input multiplied by the contribution to the uncertainty in the value of that module-input arising from the uncertainty in the value of that system-input; and
generating an output that represents a vector-valued measurement result in which the contributions to the uncertainty are combined to determine the uncertainty in the measurement result.
8. The method as claimed in claim 7 further comprising the step of calculating the uncertainty in the measurement result as the variance-covariance matrix of the multidimensional statistical distribution associated with the measurement result.