You may use the monte carlo method:

https://en.wikipedia.org/wiki/Monte_Carlo_method

Apart from Monte Carlo sampling and its different formulations, frequentist and bayesian approaches can be also useful methods.

For nonlinear systems, Monte Carlo and Bayesian methods are suitable. LPU, based on Taylor Series inserts systematic errors.

Modular (law of the propagation of uncertainty/partial derivative method and propagation of distributions/Monte Carlo simulation method) or empirical models (intra and inter/EQA/PT) could be used fulfilling GUM principles. These models requires numerical data. Generically, for the routine use I recommend empirical models and for research purpose I recommend modular models. A nice freeware for empirical determinations could be downloaded from Nordtest: http://www.syke.fi/en-us/Services/Calibration_services_and_contract_laboratory/MUkit__Measurement_Uncertainty_Kit (this is perfect if you use models from the Nordtest TR 537 guideline which is also available free from http://www.nordtest.info/index.php/technical-reports/item/handbook-for-calculation-of-measurement-uncertainty-in-environmental-laboratories-nt-tr-537-edition-3.html). Remember that modular determination requires always a reliable model equation, which is a complex task principally when it isn't already written. Empirical models use well known sources of variance (e.g., quality control data, method validation data, EQA/PT data) and assure the traceability of measurements.

If you are using non numerical data (e.g., ordinal data even when taken from an ordinal evaluation), I recommend the use of the Bayesian models (e.g., sensitivity of results, specificity of results). This models doesn't fulfill GUM principles and the uncertain concept must be viewed according. There is one article and a presentation in my RG dealing with this issue (Bayesian models) but in a different approach - screening immunoassays in blood establishments/blood bank. Anyway, it could be useful for you.

Another possibility to approach your problem might be via a set-based approach. This is not straightforward estimation, but a tool to invalidate all infeasible variables for an estimation problem. This means that you can build the set of all feasible models from a general model structure and bounded measurement data. In other words: you can find guaranteed lower and upper bounds for your parameters, such that your model structure fits your bounded (i.e. uncertain) measurement values. However this "guaranteed" values might be less informative, depending on your intended application (here you get all feasible cases, including the famous "worst case" for your parameter set, without regard to "how likely" a parameter value is). So, not precisely parameter estimation, but uncertainty bounding.

Approaches to "outer-bound" and "inner bound" the guaranteed set of parameter values can be implemented e.g. by a toolbox for Matlab, that is called ADMIT and is available via the link below.

http://ifatwww.et.uni-magdeburg.de/syst/ADMIT/

Thank you for your helpful answer.

https://www.researchgate.net/publication/258835771_Decision_making_under_uncertainty_in_energy_systems_State_of_the_art

Article Decision making under uncertainty in energy systems: State of the art

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