With increasingly complexity and diversity in both
measurements and models of the systems being measured,
there is great interest in developing flexible and efficient
means of combining all possible sources of information.
The research uses a Bayesian approach, in which it
is assumed that the a priori
probability distributions of errors in the observations and
the model forcing terms are known. The analysis can then be
taken as the field which maximises the joint probability
distribution function. This approach leads to a penalty
function which must be minimised to find the analysis.
If the error probability distribution functions are not known,
a penalty function can be constructed by analogy and used on
an ad hoc basis. In the latter case, the parameters
which would ideally be determined from the probability disributions
must be tuned to obtain smooth and physically reasonable results.
An analysis system must be able to
smooth noisy data,
interpolate sparse data,
and infer variables which are not directly measured.
The approach used here imposes the model equations as a soft constraint.