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COP4: Discrete modelling, data fusion and data fitting
To be closely aligned with activity in other COPs, particularly 3 and 6. The following are the agreed tasks and suggested sub-tasks. Task 1: Review and evaluation of algorithms and software Subtask 1.1: Algorithms and software for established discrete modelling and data fitting (e.g. using polynomials or splines). Subtask 1.2: Algorithms and software for newer univariate and multivariate empirical modelling and approximation, based on radial basis functions, wavelets, rational functions, etc. Subtask 1.3: Best practice optimisation algorithms and software for use in total least squares (TLS) and other newer approximation methods. Subtask 1.4: Algorithms and software for Gauss-Markov regression (correlation in uncertainty matrix), generalised distance regression (measurement uncertainty associated with response and explanatory variables) and generalised Gauss-Markov regression (correlation, measurement uncertainty associated with response and explanatory variables). Subtask 1.5: Parameter estimation algorithms and software, such as generalised maximum likelihood estimation appropriate for the probabilistic models used in data fusion. Subtask 1.6: Algorithms and software for feature detection in signal processing and data fusion. Subtask 1.7: Best practice optimisation algorithms and software for use in maximum likelihood approximation and generalised regression. Subtask 1.8: Automatic differentiation software tools.
Task 2: Best practice guidance Subtask 2.1: Guidance on established discrete modelling and data fitting (e.g. using polynomials or splines), reviewing current guidance material and proposing how to agree upon and then produce MetroNet approved guidance. Subtask 2.2: Guidance on newer univariate and multivariate empirical modelling and approximation, based on radial basis functions, wavelets, rational functions, etc. Subtask 2.3: Guidance on total least squares (TLS) and other newer approximation methods, and analysis of their behaviour. Subtask 2.4: Guidance on maximum likelihood approximation for more general distributions such as student t and other long-tailed distributions, and their relationship to TLS and robust estimation methods. Subtask 2.5: Guidance on incorporation of best practice optimisation algorithms into regression methods. Subtask 2.6: Guidance on probabilistic models for data fusion based on statistical models of sensor behaviour Subtask 2.7: Guidance on feature detection methods, for use in signal processing and data fusion. Subtask 2.8: Guidance on automatic differentiation methods.
Task 3: Case studies on the use of the guidance, algorithms and/or software in metrology Subtask 3.1: Case studies in established discrete modelling and data fitting. Subtask 3.2: Case studies in newer univariate and multivariate empirical modelling and approximation. Subtask 3.3: Case studies in total least squares (TLS) and other newer approximation methods. Subtask 3.4: Case studies in maximum likelihood approximation. Subtask 3.5: Case studies on regression methods (Gauss-Markov regression, generalised distance regression, generalised Gauss-Markov regression). Subtask 3.6: Case studies on use of probabilistic models for data fusion. Subtask 3.7: Case studies on applications of data fusion to metrology. Subtask 3.8: Case studies on feature detection in signal processing and data fusion. Subtask 3.9: Case studies on use of automatic differentiation methods.
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