A parameter estimation apparatus of an embodiment of the present invention is provided with a model reduction processor and a parameter estimator. The model reduction processor generates reduced order models by reducing order of a simulation model on the basis of measurement data sets and conditions for model order reduction possibility. The parameter estimator estimates values of parameters of the reduced order models on the basis of the reduced order models and the measurement data sets corresponding to the reduced order models. Further, after estimating a first value for a first parameter of a first reduced order model based on a first measurement data set, the parameter estimator applies the first value to the first parameter of a second reduced order model based on a second measurement data set.