Error and sensitivity analysis of stochastic approximation algorithms for linear system identification

Propagation of errors in identifying constant coefficient parameters of a discrete time linear system, using stochastic approximation algorithms, is investigated. Error and sensitivity analysis algorithms are derived for the cases when there is structural modeling error as well as when the a priori statistics of identified parameters, and plant and measurement noise, are incorrectly specified. The error and sensitivity analysis algorithms are useful as a design tool to better specify appropriate identification algorithms for actual implementation. The error and sensitivity analysis algorithms are applied to several examples including identification of eight predictor coefficients for adaptive digitized speech transmission.