An efficient calculation of Fisher information matrix: Monte Carlo approach using prior information

The Fisher information matrix (FIM) is a critical quantity in several aspects of system identification, including input selection and confidence region calculation. Analytical determination of the FIM in a general system identification setting may be difficult or almost impossible due to intractable modeling requirements and/or high-dimensional integration. A Monte Carlo (MC) simulation-based technique was introduced by the second author to address these difficulties (Spall, 2005). This paper proposes an extension of the MC algorithm in order to enhance the statistical qualities of the estimator of the FIM. This modified MC algorithm is particularly useful in those cases where the FIM has a structure with some elements being analytically known from prior information and the others being unknown. The estimator of the FIM, obtained by using the proposed MC algorithm, simultaneously preserves the analytically known elements and reduces the variances of the estimators of the unknown elements by capitalizing on the information contained in the known elements.