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Estimation of constant parameters in the homogeneous differential equation models of systems with time varying but bounded parameters is considered. In this case the parameter estimates can take any value within bounds. In the first order models the estimates converge to the mean values or to the weighted mean values, depending on the methodology of estimation. In the higher order models this problem may be more complicated. For the periodically varying parameters a good policy to estimate the mean value is to observe the system with the constant period of parameters variation. Other observation schema may conduce not only to biased estimates of the parameters but also to biased estimate of the system order when it is estimated statistically. Examples of modelling problems connected with the varying parameters encountered in real systems are presented.
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Projects co-financed by:
Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.