The Fisher information matrix for linear systems

✍ Scribed by Raimund J. Ober

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 107 KB
• Volume: 47
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(02)00190-1

✦ Synopsis

Estimation of parameters of linear systems is a problem often encountered in applications. The Cramer Rao lower bound gives a lower bound on the variance of any unbiased parameter estimation method and therefore provides an important tool in the assessment of a parameter estimation method and for experimental design. Here we study the calculation of the Fisher information matrix, the inverse of the Cramer Rao lower bound, from a system theoretic point of view. A number of results appear in the literature that deal with the case where the stationary data is given as the output of a linear system driven by Gaussian noise. The non-stationary situation where the data is the output of a linear system with Gaussian measurement noise is rarely considered despite its importance in applications. A general description will be given for Fisher information for such data in terms of a derivative system. For a uniformly sampled data set of impulse response type a closed form expression can be given for the Fisher information using the solution of a Lyapunov equation.